Of  THE 

UHIVP^,ty  Of  ''-UNO*3 


The  University  of  Chicago 


The  Freezing  Point  Lowerings  of  Mixtures 
and  in  Solutions  of  Cobaltammines,  and 
Other  Salts  of  Various  Types 
of  Ionization 


The  Periodic  System  and  the  Properties  of  the 

Elements 


A DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  OGDEN  GRADUATE 
SCHOOL  OF  SCIENCE  IN  CANDIDACY  FOR  THE  , 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

(DEPARTMENT  OF  CHEMISTRY) 


By  Ralph  E*  Hall 


(t*s,ry  '*3/ 


A Private  Edition 
Distributed  by 

The  University  of  Chicago  Libraries 


ESCHENBACH  PRINTING  COMPANY 
EASTON,  PA. 


5 v/'4? 


The  Periodic  System  and  the  Properties 

the  Elements. 


The  periodic  system  is  the  most  important  generalization  of  the  facts 
embodied  in  the  science  of  chemistry,  and  one  of  the  most  glaring  errors 
in  chemical  pedagogy  during  the  past  fifteen  years  has  been  the  neglect 
of  this  system,  both  in  the  so-called  modern  text-books  and  in  the  courses 
of  instruction  given  in  some  of  our  universities.  This  has  probably  been 
due,  in  a large  measure,  to  the  unfortunate  attempt  which  has  been  made 
by  certain  chemists  to  present  chemistry  without  the  use  of  the  atomic 
theory.  Recent  remarkable  discoveries  made  by  physicists  have,  how- 
ever,. made  it  evident  that  the  atomic  theory  and  the  periodic  system 
are  of  supreme  importance  in  both  chemistry  and  physics. 

The  total  number  of  elements  in  our  present  ordinary  system  from 
helium  to  uranium,  inclusive,  is  91,  and  with  hydrogen  this  makes  92 
elements  in  all.  The  system  from  helium  to  uranium  seems  to  be  com- 
pletely known,  though  not  all  of  the  elements  have  been  discovered, 
but  nothing  is  known  as  to  whether  there  are  any  elements  which  belong 
to  the  ordinary  system  and  fall  between  hydrogen  and  helium  in  atomic 

[Reprinted  from  an  article  by  W.  D.  Harkins  and  R.  E.  Hall  in  the  Journal  of  the 
American  Chemical  Society  for  February,  1916.] 


58787 


4 


weight  (possibly  with  atomic  weights  2 and  3).  Of  the  92  elements,  87 
have  already  been  discovered  and  5 are  still  unknown.  Of  these  5,  three 
belong  to  the  seventh  group,  two  being  in  group  VIIB,  and  these  may 
be  given  the  provisional  names  eka-manganese  I (atomic  weight  about 
99),  and  eka  manganese  II  (divi-manganese)  (atomic  weight  about  188). 
These  elements,  particularly  the  second,  should  have  extremely  high  melt- 
ing points.  In  group  VIIA  eka-iodine  should  have  an  atomic  weight  near 
219,  and  in  group  I A eka-caesium,  for  which  Baxter  made  a search,  but 
without  success,  should  have  an  atomic  weight  of  about  225.  An  unknown 
element  of  the  rare  earth  group  may  be  called  eka-neodymium  (atomic 
weight  about  146). 

In  addition  to  these  92  elements  of  the  ordinary  system,  Nicholson 
assumes  that  there  is  another  system  of  simpler  elements  such  as  proto- 
hydrogen, nebulium,  protofluorine  (coronium),  arconium,  and  other  ele- 
ments, of  atomic  weights  0.082,  1.31,  2.1,  and  2.9.  Of  these  elements 
the  spectra  attributed  to  nebulium  and  arconium  are  found  in  the  nebula 
and  that  of  the  hypothetical  protofluorine  is  found  in  the  corona  of  the 
sun.  The  evidence  in  favor  of  this  simpler  system  is  not  very  conclusive, 
but  the  existence  of  these  spectra  makes  it  evident  either  that  some  other- 
wise unknown  elements  exist  in  the  nebulae  and  the  corona  of  the  sun 
or  that  the  spectra  are  due  to  enhanced  lines  from  some  of  the 
ordinary  elements.1  If  such  elements  actually  exist,  they  may  belong 
to  the  ordinary  system,  or  they  may  belong  to  another  system,  possibly 
with  a simpler  structure  as  Nicholson  assumes.  Nicholson’s  atomic 
weights  were  obtained  from  the  width  of  the  spectral  lines,  and  also  from 
the  differences  between  the  calculated  and  the  observed  values  of  the 
wave  lengths.  Both  of  these  methods  are  very  uncertain  under  the  con- 
ditions of  observation,  so  there  is  no  conclusive  evidence  for  the  particu- 
lar atomic  weights  which  Nicholson  gives.2 

It  has  been  found  that  the  number  of  the  element  in  the  periodic  table, 
beginning  with  hydrogen  as  1,  helium  as  2,  lithium  as  3,  etc.;  or  what  is 
called  the  atomic  number  is  more  characteristic  of  an  element  than  its 
atomic  weight.  For  example  lead,  with  an  atomic  number  of  82,  con- 
sists of 

Atomic  weight. 


1.  Lead  from  radium 206.1 

2.  Ordinary  lead 207.20 

3.  Lead  from  thorium 208.1 


1 Merton,  Proc.  Roy.  Soc.,  ( A ) 91,  498  (1915),  has  obtained  enhanced  lines  by  a 
discharge  between  carbon  poles  in  a vacuum  tube,  previously  filled  with  hydrogen, 
which  have  practically  the  same  wave  length,  and  the  same  nebulous  character  as 
eight  of  the  lines  obtained  in  the  spectrum  of  the  Wolf-Rayet  stars. 

2 For  a more  complete  description  and  discussion  of  Nicholson’s  work  see  a paper 
on  “Recent  Work  on  the  Structure  of  the  Atom,’’  Harkins  and  Wilson,  J.  Am.  Chem. 
Soc.,  37,  1396-1421  (1915). 


Note,  Fig.  i. — The  connections  between  the  main  and  the  sub- 
groups are  shown  better  in  Fig.  2 than  in  Fig.  1,  since  in  Fig. 
1 the  connections  were  modified  slightly  by  the  artist  to  bring 
out  the  perspective. 


Fig.  2. 


5 


Atomic  weight. 


4.  Radium  D 210. 1 

5.  Thorium  B 214. 1 

6.  Radium  B 212. 1 

7.  Lead  from  actinium Unknown 

8.  Lead  from  actinium  B Unknown 

9.  Product  of  branch  chain,  radium  series 210. 1 

10.  Product  of  branch  chain,  actinium  series Unknown 


Thus  the  same  element  may  have  very  widely  different  atomic  weights, 
but  the  atomic  number,  which  presumably  gives  the  number  of  positive 
charges  on  the  nucleus  of  the  atom,  remains  constant,  and  in  the  case  of 
lead  is  82. 

A Periodic  Table  which  Gives  all  of  the  Elements  Plotted  According  to 
Their  Atomic  Weights,  and  Shows  the  Correct  Relations 
from  the  Chemical  Standpoint. 

The  periodic  system  of  Mendeleeff  classified  the  elements  as  well  as 
was  possible  at  the  time  when  it  was  devised,  and  practically  none  of  the 
more  recent  tables  have  made  any  improvement  upon  the  original  form, 
but  the  discoveries  of  the  last  few  years  make  it  possible  to  design  a table 
which  expresses  the  relations  existing  between  the  elements  much  more 
perfectly. 

A modern  table  should  meet  the  following  requirements: 

(1)  It  should  plot  the  atomic  weights  so  that  the  isotopes  of  such  an 
element  as  lead  may  be  included  in  it,  their  atomic  weights  shown,  and 
so  that  the  alpha  and  beta  decompositions  of  the  radioactive  elements 
may  be  clearly  depicted. 

(2)  It  should  give  no  blanks  except  those  corresponding  to  atomic 
numbers  of  elements  which  remain  to  be  discovered.  The  Mendeleeff 
table  contains  many  blanks  which  can  never  be  filled. 

(3)  It  should  in  a natural  way  relate  the  main  group  elements  to  the 
' elements  in  the  corresponding  sub-group.  The  principal  defect  of  many 

of  the  periodic  tables  is  that  they  have  been  constructed  without  any 
consideration  of  this  important  condition.  A table  which  shows  no  rela- 
tions between  such  a main  group  as  the  Be,  Mg,  Ca,  Sr,  Ba  and  Ra  main 
group,  and  the  corresponding  sub-group,  Zn,  Cd,  Hg,  is  not  at  all  correct 
from  the  chemical  standpoint.  On  the  other  hand,  the  form  of  the  table 
itself  should  distinguish  between  the  main  and  the  sub-group  elements. 
One  of  the  disadvantages  of  the  Mendeleeff  table  is  that  the  table  by  its 
form  makes  no  such  distinction,  since  it  throws  the  main  and  sub-groups 
together.  However,  the  Mendeleeff  form  is  much  to  be  preferred  to  those 
given  by  Staigmiiller,  Werner  and  others,  in  which  these  chemical  rela- 
tions are  not  shown  at  all. 

(4)  Both  the  zero  and  the  eighth  groups  should  fit  naturally  into  the 
system. 


6 


(5)  All  of  the  above  relations  should  be  shown  by  a continuous  curve 
which  should  connect  the  elements  in  the  order  of  their  atomic  numbers. 
In  the  ordinary  form  of  table  there  is  nothing  to  indicate  the  relation  of 
one  series  to  the  next. 

(6)  As  has  been  shown  by  Harkins  and  Wilson,  the  atomic  weights 
are  a linear  function  of  the  atomic  numbers,  and  can  be  represented  by 
the  equation 

W = 2 (n  + n')  + 1/2  + i/2(  — i)”-1, 
where  n is  the  atomic  number  and  n'  is  ZERO  for  the  lighter  ELEMENTS. 
It  is  therefore  better  to  plot  the  atomic  weights  themselves  than  to  plot 
the  logarithms  as  has  been  done.1 

A modern  table  which  meets  these  requirements  and  also  shows  other 
relationships  not  expressed  by  the  ordinary  form  of  table,  may  be  con- 
structed as  a helix  in  space,  or  as  a spiral  on  a plane.  The  space  form  is 
more  nearly  like  the  ordinary  table,  and  is  therefore  to  be  preferred.  A 
model  of  this  space  form,  a photograph  of  which  is  shown  in  Fig.  3, 
has  been  constructed,  and  is  in  use  in  the  work  in  inorganic  chemistry 
in  the  University  of  Chicago.  The  atomic  weights  are  plotted  from  the 
top  down,  one  unit  of  atomic  weight  being  represented  by  one  centimeter, 
so  the  model  is  about  two  and  one- half  meters  high. 

Although  the  model  gives  the  relations  with  extreme  clearness,  it  is 
difficult  to  photograph  it  so  that  all  of  the  details  are  visible.  However, 
this  is  remedied  in  Fig.  1,  which  gives  a drawing  of  the  system.  In 
order  that  the  atomic  weights  may  be  plotted  directly,  the  drawing  has 
been  made  as  a vertical  projection  of  the  model,  but  drawn  with  line  per- 
spective, and  the  base  is  given  in  perspective  so  that  the  table  may  be 
easily  visualized  in  space. 

The  balls  representing  the  elements  are  supposed  to  be  strung  on  vertical 
rods.  All  of  the  elements  on  one  vertical  rod  belong  to  one  group,2  have 
on  the  whole  the  same  maximum  valence,  and  are  represented  by  the  same 
color.  The  group  numbers  are  given  at  the  bottom  of  the  rods.  On  the 
outer  cylinder  in  Fig.  2,  the  electro-negative  elements  are  represented 
by  black  circles  at  the  back  of  the  cylinder,  and  electro-positive  elements 
by  white  circles  on  the  front  of  the  cylinder.  The  transition  elements 

1 Stoney,  Chem.  News,  57,  163  (1888);  and  Proc.  Roy.  Soc.,  46,  115  (1888). 

2 In  Figs.  1 and  2 some  of  the  elements  are  represented  by  small,  and  others  by 
larger  circles.  The  small  circles  are  not  meant  to  show  any  difference  in  the  elements 
which  they  represent,  but  are  used  whenever  there  is  not  room  on  the  diagram  for  the 
larger  circles.  At  the  bottom  of  the  table  many  isotopes  are  represented,  and  each 
intersection  of  the  helix  with  a vertical  group  rod  represents  only  one  element,  even 
where  there  arc  six  circles  as  there  are  for  the  isotopes  of  lead.  While  the  six  circles 
for  lead  represent  only  one  atomic  number,  each  of  the  small  circles  on  the  rare  earth 
loop  represents  an  atomic  number  of  its  own.  The  three  eighth  group  triads,  and  the 
rare  earth  group  resemble  each  other  in  that  in  these  four  cases  the  atomic  number 
increases  while  the  group  number  remains  constant. 


r 


of  the  zero  and  fourth  groups  are  represented  by  circles  which  are  half 
black  and  half  white.  The  inner  loop  elements  are  intermediate  in  their 
properties.  Elements  on  the  back  of  the  inner  loop  are  shown  as  heavily 
shaded  circles,  while  those  on  the  front  are  shaded  only  slightly. 

In  order  to  understand  the  table  it  may  be  well  to  take  an  imaginary 
journey  down  the  helix  in  Fig.  2,  beginning  at  the  top.  Hydrogen 
(atomic  number  and  atomic  weight  = 1)  stands  by  itself,  and  is  followed 
by  the  first  inert,  zero  group,  and  zero  valent  element  helium.  Here 
there  comes  the  extremely  sharp  break  in  chemical  properties  with  the 
change  to  the  strongly  positive,  univalent  element  lithium,  followed  by 
the  somewhat  less  positive  bivalent  element,  beryllium,  and  the  third 
group  element  boron,  with  a positive  valence  of  three,  and  a weaker 
negative  valence.  At  the  extreme  right  of  the  outer  cylinder  is  carbon, 
the  fourth  group  transition  element,  with  a positive  valence  of  four, 
and  an  equal  negative  valence,  both  of  approximately  equal  strength. 
The  first  element  on  the  back  of  the  cylinder  is  more  negative  than  posi- 
tive, and  has  a positive  valence  of  five,  and  a negative  valence  of  three. 
The  negative  properties  increase  until  fluorine  is  reached  and  then  there 
is  a sharp  break  of  properties,  with  the  change  from  the  strongly  nega- 
tive, univalent  element  fluorine,  through  the  zero  valent  transition  ele- 
ment neon,  to  the  strongly  positive  sodium  Thus  in  order  around  the 
outer  loop  the  second  series  elements  are  as  follows : 


Group  number o 1 2 3 4 5 6 7 

Maximum  valence o 1 2 3 4 5 6 7 

Element He  Li  Be  B C N O F 

Atomic  number 2 3 4 5 6 7 8 9 


After  these  comes  neon,  which  is  like  helium,  sodium  which  is  like 
lithium,  etc.,  to  chlorine,  the  eighth  element  of  the  second  period.  For  the 
third  period  the  journey  is  continued,  still  on  the  outer  loop,  with  argon, 
potassium,  calcium,  scandium,  and  then  begins,  with  titanium,  to  turn 
for  the  first  time  into  the  inner  loop.  Vanadium,  chromium,  and  man- 
ganese, which  come  next,  are  on  the  inner  loop,  and  thus  belong,  not  to 
main  but  to  sub-groups.  This  is  the  first  appearance  in  the  system  of  sub- 
group elements.  Just  beyond  manganese  a catastrophe  of  some  sort 
seems  to  take  place,  for  here  three  elements  of  one  kind,  and  therefore 
belonging  to  one  group,  are  deposited.  The  eighth  group  in  this  table 
takes  the  place  on  the  inner  loop  which  the  rare  gases  of  the  atmosphere 
fill  on  the  outer  loop.  The  eighth  group  is  thus  a sub-group  of  the  zero 
group. 

After  the  eighth  group  elements,  which  have  here  appeared  for  the  first 
time,  come  copper,  zinc,  and  gallium;  and  with  germanium,  a fourth 
group  element,  the  helix  returns  to  the  outer  loop.  It  then  passes  through 
arsenic,  selenium,  and  bromine,  thus  completing  the  first  long  period  of 


8 


1 8 elements.  Following  this  there  comes  a second  long  period,  exactly 
similar,  and  also  containing  18  elements. 

The  relations  which  exist  may  be  shown  by  the  following  natural  classi- 
fication of  the  elements.  They  may  be  divided  into  cycles  and  periods 
as  follows: 

Table  I. 

Cycle  i = 42  elements. 

ist  short  period He  — F = 8 = 2 X 22  elements. 

2nd  short  period Ne  — Cl  = 8 = 2 X 22  elements. 

Cycle  2 = 62  elements. 

1 st  long  period A — Br=  18  =2  X32  elements. 

2nd  long  period Kr  — I = 18  = 2 X32  elements. 

Cycle  3 = 82  elements. 

ist  very  long  period. . . Xe  — Eka  - I = 32  = 2 X 42  elements. 

2nd  very  long  period. . . Nt  — U 

The  last  very  long  period,  and  therefore  the  last  cycle,  is  incomplete. 
It  will  be  seen,  however,  that  these  remarkable  relations  are  perfect  in 
their  regularity.  These  are  the  relations,  too,  which  exist  in  the  com- 
pleted system,1  and  are  not  like  many  false  numerical  systems  which  have 
been  proposed  in  the  past  where  the  supposed  relations  were  due  to  the 
counting  of  blanks  which  do  not  correspond  to  atomic  numbers.  This 
peculiar  relationship  is  undoubtedly  connected  with  the  variations  in 
structure  of  these  complex  elements,  but  their  meaning  will  not  be  ap- 
parent until  we  know  more  in  regard  to  atomic  structure. 

The  first  cycle  of  two  short  periods  is  made  up  wholly  of  outer  loop  or 
main  group  elements.  Each  of  the  long  periods  of  the  second  cycle  is 
made  up  of  main  and  of  sub-group  elements,  and  each  period  contains 
one  eighth  group.  The  only  complete  very  long  period  is  made  up  of  main 
and  of  sub-group  elements,  contains  one  eighth  group,  and  would  be  of 
the  same  length  (18  elements)  as  the  long  periods  if  it  were  not  lengthened 
to  32  elements  by  the  inclusion  of  the  rare  earths. 

The  first  long  period  is  introduced  into  the  system  by  the  insertion  of 
iron,  cobalt,  and  nickel,  in  its  center,  and  these  are  three  elements  whose 
atomic  numbers  increase  by  steps  of  one  while  their  valence  remains  con- 
stant. The  first  very  long  period  is  formed  in  a similar  way  by  the  in- 
sertion of  the  rare  earths,  another  set  of  elements  whose  atomic  numbers 
increase  by  one  while  the  valence  remains  constant. 

In  this  periodic  table  the  maximum  valence  for  a group  of  elements 
may  be  found  by  beginning  with  zero  for  the  zero  group  and  counting 

1 If  elements  of  atomic  weights  two  and  three  are  ever  discovered  then  the  zero 
cycle  would  contain  2 2 elements,  and  period  number  one  should  then  be  said  to  begin 
with  lithium.  Such  extrapolation,  however,  is  an  uncertain  basis  for  the  prediction 
of  such  elements. 


IhL  USRAliY 
Of  ih£ 


1 


H 


1.0078 


Periodic  System  of  the  Elements  by  W.  D.  Harkins  and  R E.  Hall 
(Arranged  according  to  the  Atomic  Numbers] 


/ 


Periods 

Group 

O 

Group 
A I 

RiO 

B 

Group 
A II 

RO 

B 

Group 

A III  B 

R2O3 

A 

Group 

IV  B 

ROj.  RHi 

Group 

B V A 

RiO.lRHi 

Group 

B VI  A 

ROj,  R Hi 

Group 

B VII  A 
R1O7.RH 

Group 

VIII 

RO« 

2 

3 

4 

5 

6 

7 

8 

9 

i 

He 

Li 

Be 

B 

C 

N 

O 

F 

4.00 

6.94 

9. 1 

11.0 

1 2 . 005 

14.01 

16.00 

19.0 

10 

11 

12 

13 

14 

15 

16 

17 

2 

Ne 

Na 

Mg 

A1 

Si 

P 

S 

Cl 

20.2 

23 . 00 

24.32 

27.  1 

28.3 

31.04 

32.06 

35 . 46 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

A 

K 

Ca 

Sc 

Ti 

V 

Cr 

Mn 

Fe 

Co 

Ni 

3 

39.88 

39. 10 

40.07 

44  1 

48 

1 

51.0 

52.0 

54.93 

55.84 

58.97 

58 . 68 

29 

30 

31 

32 

33 

34 

35 

[He, Co, Nil 

Cu 

Zn 

Ga 

Ge 

As 

Se 

Br 

63 

.57 

65 

37 

69.9 

72.5 

74.96 

79.2 

79.92 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

Kr 

Rb 

Sr 

Yt 

Zr 

Cb 

Mo 

— 

Ru 

Rh 

Pd 

4 

82.92 

85 . 45 

87 . 63 

88.7 

90 

6 

93  5 

96.0 

101.7 

102.9 

106.7 

47 

48 

49 

50 

51 

52 

53 

[Ru.Rh.Pd] 

Ag 

Cd 

In 

Sn 

Sb 

Te 

I 

107.88 

112.40 

114.8 

118  7 

120.2 

127.5 

126.92 

54 

55 

56 

57  La 

139.0 

58 

Xe 

Cs 

Ba 

Ce 

130.2 

132.81 

137.37 

59  Pr 

140.9 

1 40 . 25 

60  Nd 

61  — 

144.3 

62  Sa 

150.4 

63  Eu 

152.0 

64  Gd 

157.3 

5 

65  Tb 

159.2 

66  Dy 

162.5 

67  Ho 

163.5 

68  Er 

167.7 

69  Tmj 

70  T m2 

168.5 

71  Yb 

1 73 . 5 

73 

74 

75 

76  77 

78 

72  Lu 

175.0 

Ta 

w 

— 

Os  Ir 

Pt 

181.5 

184  0 

190.9  193.1 

195.2 

79 

80 

81 

82  ’ 

83 

84 

85 

(Os.Ir.Pt  ] 

Au 

Hg 

Tl 

Pb 

Bi 

Po 

197.2 

200.6 

204.0 

207 . 20 

208  0 

210.0  | 

86 

87 

88 

89 

90 

91 

92 

6 

Nt 

— 

Ra 

Ac 

Th 

Bv 

U 

222.4 

226  0 

232.2 

234  2 

238  2 

4 4 3 

I I 

1 

Divisions 


1 

2 

J 


I 


I 


0 


0 


9 


toward  the  front  for  positive  valence,  and  toward  the  back  for  negative 
valence. 

The  negative  valence  runs  along  the  spirals  toward  the  back  as  follows: 

o — i — 2 — 3 — 4 

Ne  F O N C 

A Cl  S P Si 

Beginning  with  helium  the  relations  of  the  maximum  theoretical  val- 
ences run  as  follows : " 

Case  i.  He  — F o,  i,  2,  3,  4,  5,  6,  7,  but  does  not  rise  to  8.  Drops  by  7 to  o. 

Ne  — Cl.  . . . o,  1,  2,  3,  4,  5,  6,  7,  but  does  not  rise  to  8.  Drops  by  7 to  o. 
Case  2.  A — Mn.  ...  o,  1,  2,  3,  4,  5,  6,  7,  8,  8,  8.  Drops  by  7 to  1. 

Fe.  Co,  Ni. 

Case  1 . Cu  — Br 

Case  2.  Kr  — Ru,  Rh,  Pd. 

In  the  third  increase,  the  group  number  and  maximum  valence  of 
the  group  rise  to  8,  three  elements  are  formed,  and  the  drop  is  again  by 
7 to  1. 

Thus  in  every  case  when  the  valence  drops  back  the  drop  in  maximum 
group  valence  is  7,  either  from  7 to  o,  or  from  8 to  i.1  This  is  another 
illustration  of  the  fact  that  the  eighth  group  is  a sub-group  of  the  zero 
group.  The  valence  of  the  zero  group  is  zero.  According  to  Abegg 
the  contra-valence,  seemingly  not  active  in  this  case,  is  eight. 

In  Fig.  2 the  table  is  divided  into  five  divisions  by  four  straight 
lines  across  the  base.  These  divisions  contain  the  following  groups: 


Division o 1 2 3 4 

Groups 0,8  1,7  2,6  3,5  4,4 


The  two  groups  of  any  division  are  said  to  be  complementary.  It  will 
be  seen  that  the  sum  of  the  group  numbers  in  any  division  is  equal  to  8, 
as  is  also  the  sum  of  the  maximum  valences.  The  algebraic  sum  of  the 
characteristic  valences  of  two  complementary  groups  is  always  zero. 
In  any  division  in  which  the  group  numbers  are  very  different , the  chemical 
properties  of  the  elements  of  the  complementary  main  groups  are  very  differ- 
ent, but  when  the  group  numbers  become  the  same,  the  chemical  properties 
become  very  much  alike.  Thus  the  greatest  difference  in  group  numbers 
occurs  in  division  8,  where  the  difference  is  8,  and  in  the  two  groups  there 
is  an  extreme  difference  in  chemical  properties,  as  there  is  also  in  division 
1 between  Groups  1 and  7.  Whenever  the  two  main  groups  of  a division 
are  very  different  in  properties , each  of  the  sub-groups  is  quite  different  from 

1 It  should  be  noted  that  while  in  the  change  from  the  seventh  to  the  zero  group 
the  valence  always  drops  to  zero,  in  the  change  from  the  eighth  to  the  IB  group,  there 
is  a tendency  to  drop  only  part  way,  that  is  to  a valence  of  3 for  gold  (or  silver),  or 
to  2 for  copper,  though  these  elements  also  show  the  valence  of  one  normal  for  the 
group,  but  by  the  time  Group  IIB  is  reached  in  zinc,  cadmium,  and  mercury,  the 
valence  comes  to  the  normal  value,  which  is  2 for  this  group. 


IO 


its  related  main  group.  Thus  copper  in  Group  IB  is  not  very  closely  re- 
lated to  potassium  group  IA  in  its  properties,  and  manganese  is  not 
very  similar  to  chlorine,  but  as  the  group  numbers  approach  each  other 
the  main  and  sub-groups  become  much  alike.  Thus  scandium  is  quite  sim- 
ilar to  gallium  in  its  properties,  and  titanium  and  germanium  are  very 
closely  allied  to  silicon. 

One  important  relation  is  that  on  the  outer  cylinder  the  main  groups 
I A,  II  A,  III  A,  become  less  positive  as  the  group  number  increases , while  on 
the  inner  loop  the  positive  character  increases  from  Group  IB  to  IIB , and 
at  the  bottom  of  the  table  the  increase  from  IIB  to  IIIB  is  considerable. 
Thus  thallium  is  much  more  positive  than  mercury.  It  has  already  been 
noted  that  in  the  case  of  the  rare  earths  also  the  usual  rule  is  inverted, 
that  is  the  basic  properties  decrease  as  the  atomic  weight  increases. 

Another  important  relation  between  the  members  of  the  main  and  the 
sub-groups  is  that  when  the  atomic  volume  of  the  elements  in  the  main 
group  is  large,  the  atomic  volume  of  the  elements  in  the  corresponding 
sub-groups  is  small,  and  as  the  atomic  volume  for  the  main  group  de- 
creases, that  for  the  sub-group  increases.  Thus,  the  zero  group  elements 
have  very  high  atomic  volumes,  while  those  for  the  corresponding  sub- 
groups (Group  VIII)  are  very  low.  The  same  is  true  of  the  potassium 
group  (high  atomic  volume)  and  the  copper  group  (low  atomic  volume). 
On  the  other  hand,  the  members  of  Groups  IVA  and  IVB  do  not  differ 
materially  in  regard  to  this  property.  The  difference  in  chemical  proper- 
ties between  main  and  sub-groups  is  just  that  which  should  result  from 
their  differences  in  atomic  volume.  From  this  standpoint  it  may  be  con- 
sidered that  the  difference  in  chemical  properties  between  the  main  and 
the  sub-group  elements  is  the  result  of  the  fact  that  the  long  periods 
for  the  cohesional  properties  (atomic  volume,  etc.)  are  twice  the  length 
of  the  series  which  condition  the  valence.  In  cycle  i (short  periods  i 
and  2),  the  valence  and  the  cohesional  properties  have  periods  of  exactly 
the  same  length,  so  both  of  the  periods  represent  main  groups  or  outer 
cylinder  elements,  but  in  cycle  2 the  valence  passes  through  two  periods 
while  the  cohesion  (Fig.  12)  is  passing  through  one,  so  here  sub-group 
elements  appear  for  the  first  time.  While  the  cohesion  does  not  fix  the 
valence,  it  does  affect  the  chemical  affinity.  The  increase  in  the  basic 
properties  of  the  sub-group  elements  as  the  group  number  increases  from 
IB  to  IIIB,  seems  to  be  related  to  the  occurrence  of  the  secondary  mini 
mum  in  cohesion  (and  melting  points)  which  comes  in  group  IIIB.  (See 
Fig.  8.) 

On  the  first  inner  loop  the  positive  character  of  the  metal,  as  measured 
by  the  potential  between  the  ions  of  the  elements  in  unimolar  solutions 
and  the  metal  itself,  decreases  from  manganese  to  copper,  and  then  in- 
creases very  rapidly  in  the  one  step  to  zinc,  as  is  shown  below  in  Table  IA. 


1 1 

Table  Id. — Positive  Character  of  the  Metals  in  Solutions  with  Their 

Bivalent  Ions. 

Mn  = +0.798  volt 
Fe  = +0. 122  volt 
Co  = — 0.0138  volt 
Ni  = — o . 108  volt 
Cu  = — 0.606  volt 
Zn  = +0.493  volt 

The  Rare  Earths. 

There  are  some  questions  concerning  the  placing  of  the  rare  earth  ele- 
ments which  are  of  minor  importance,  and  may  be  settled  by  each  user 
of  such  a table  to  suit  his  own  convenience.  Thus  cerium,  following 
the  usual  custom,  has  been  put  in  the  fourth  group.  This  makes  an  extra 
small  loop  in  the  table  which  could  be  avoided  by  placing  cerium  in  the 
third  group  with  the  other  rare  earths.  That  after  passing  lanthanum 
there  is  a tendency  to  swing  into  the  fourth  group  with  cerium,  and  then 
with  praseodymium  and  neodymium  to  swing  back  into  the  third  group, 
is  indicated  by  the  fact  that  cerium  forms  an  extremely  stable  dioxide 
(CeCb);  praseodymium  forms  a dioxide  less  stable  than  manganese  di- 
oxide, which  is  itself  not  extremely  stable;  while  neodymium  is  said  to 
form  a higher  oxide  only  when  mixed  with  cerium  and  praseodymium, 
or  perhaps  not  at  all;  and  samarium  forms  no  higher  oxide. 

On  the  other  hand,  the  position  of  the  rare  earths  as  a whole  is  very 
important.  Their  valence,  the  difficulty  with  which  they"  are  separated 
from  yttrium,  and  their  chemical  reactions  clearly  indicate  that  they  should 
be  related  to  the  third  group,  but  put  on  a loop  of  their  own.  In  many 
periodic  tables,  for  example,  even  in  the  otherwise  very  good  table  given 
by  Rydberg,1  thulium  is  put  in  the  chlorine  family,  samarium  in  the 
eighth  group,  europium  in  the  silver  group,  etc.  The  system  presented 
here  shows  that  such  a procedure  is  altogether  unjustified,  for  there  are 
not  enough  rare  earths  to  go  around  the  table,  since  there  are  four  less 
than  the  required  number , even  when  the  one  unknown  rare  earth  is  counted. 
That  the  number  of  elements  in  this,  the  fifth  period,  is  taken  correctly 
as  32  can  be  seen  from  the  work  of  Moseley  upon  the  X-ray  spectra  of 
the  elements,  and  is  indicated  also  by  the  regularity  in  the  numerical 
relations  between  the  number  of  elements  in  the  different  periods  as  al- 
ready pointed  out  by  Table  I.  If  the  rare  earths  are  to  be  distributed 
around  the  table,  then  there  should  be  a considerable  variation  in  their 
atomic  volumes.  Although  the  atomic  volumes  of  very  few  of  the  rare 
earths  have  been  determined,  the  data  are  available  for  the  calculation 
of  the  molecular  volumes  of  a number  of  the  chlorides  and  oxides.  Thus 
the  molecular  volumes  of  the  chlorides  are  as  follows : 

1 Hicks,  Phil.  Mag.,  [6]  28,  139  (1914). 


12 


LaCls. 

CeCl3. 

PrCl3. 

NdCl3 

SmCl3 

GdCla 

TbCl3. 

DyCl3 


In  order  to  understand  the  interpretation  of  these  molecular  volumes 
in  terms  of  the  atomic  volumes  of  the  rare  earths,  their  basic  properties 
must  be  taken  into  account.  The  order  of  the  rare  earths  in  terms  of 
their  basic  properties  is  as  follows,  where  the  most  basic  element  is  given 
first:  Lanthanum,  praseodymium,  neodymium,  cerium111,  (yttrium), 
samarium,  gadolinium,  terbium,  holmium,  erbium,  thulium,  and  ytter- 
bium. Thus,  exactly  the  opposite  of  the  usual  rule  holds,  for  in  this 
rare  earth  group  the  basic  properties  decrease  just  in  the  order  in  which 
the  atomic  weights  increase.  Cerium  is  the  only  element  which  falls 
out  of  the  regular  order,  and  it  is  the  element  which  in  the  table  (Fig.  2) 
is  classified  differently  from  the  others.  If  the  rare  earth  elements  were 
to  be  distributed  around  the  table,  then  samarium,  europium,  and  gado- 
linium would  fall  in  the  eighth  group,  and  therefore  should  have  minimum 
atomic  volumes.  That  these  are  the  elements  of  the  rare  earths  which 
do  have  minimum  atomic  volumes  is  indicated  by  the  molecular  volumes  of 
the  chlorides.  The  increase  in  the  molecular  volume  of  the  chlorides 
in  the  case  of  dysprosium  chloride  seems  to  indicate  that  there  is  a minor 
peak  in  the  atomic  volumes  beyond  this  point.  It  would  be  interesting 
in  this  connection  to  know  the  molecular  volumes  of  ytterbium  and  lute- 
cium trichlorides,  or  much  better  of  course,  the  atomic  volumes  of  ytter- 
bium and  lutecium.  These  facts  may  be  taken  to  indicate  that  when  in 
the  formation  of  the  elements  the  57th  element,  lanthanum,  belonging  to 
the  third  group,  is  passed,  there  is  a tendency  for  the  elements  to  form  ac- 
cording to  the  usual  rule,  that  is,  that  the  valence  shall  increase  by  steps 
of  one  and  the  atomic  volume  shall  vary  as  usual.  From  this  point  on, 
the  tendency  for  the  atomic  volumes  to  hold  to  the  regular  system  of 
variation  is  quite  likely  partly  effective.  On  the  other  hand,  the  valence 
succeeds  only  in  rising  by  one  to  four  in  the  case  of  cerium,  the  58th  ele- 
ment, and  then  only  for  a few  of  its  compounds.  With  praseodymium 
and  neodymium  the  valence  returns  toward  three,  and  for  samarium 
and  the  remainder  of  the  group  the  highest  valence  seems  to  be  constant 
at  three.  Such  relationships  as  these  need  not  seem  peculiar,  since  the 
valence  is  usually  supposed  to  be  due  to  only  a few  of  the  electrons  in 
the  atom,  in  this  case  to  three  electrons,  while  the  atomic  volumes  are  un- 
doubtedly conditioned  by  the  other  electrons  in  the  atom,  external  to 
the  nucleus,  as  well.  That  the  atomic  volumes  do  not  wholly  follow 


13 


the  ordinary  rule  is  shown  by  the  fact  that  the  atomic  volumes  of  samarium, 
europium,  and  gadolinium  do  not  fall  nearly  so  low  as  the  ordinary  eighth 
group  elements. 

The  exceptional  behavior  of  the  rare  earths  in  regard  to  their  basic 
properties  may  be  explained  in  somewhat  the  same  way  as  the  probable 
atomic  volume  relations.  Just  before  coming  to  the  rare  earths  the  basic 
properties  decrease  rapidly  from  caesium,  to  barium,  and  to  lanthanum. 
This  decrease  persists  through  the  rare  earth  loop,  which  may  be  called 
a tertiary  loop,  but  probably  the  opposing  tendency,  that  is  for  the  ele- 
ments of  any  one  main  group  to  increase  in  basic  properties,  also  has  an 
effect,  for  the  rare  earths  do  not  decrease  in  basic  properties  with  any- 
thing like  the  rapidity  which  would  be  apparent  if  they  were  distributed 
around  the  table  in  the  order  of  the  other  elements.1  If  they  were  thus 
distributed,  either  ytterbium  or  lutecium  should  be  chemically  similar 
to  iodine,  and  that  is  not  the  case.  The  elements  on  the  outer  cylinder 
in  Table  I may  be  said  to  be  on  primary  loops,  the  inner  loops  may  be 
designated  as  secondary,  and  the  rare  earths  as  a tertiary  loop.  This 
tertiary  loop  connects  lanthanum  and  cerium  to  tantalum,  and  could  be 
drawn  inside  the  outer  cylinder,  but  since  the  valence  of  the  rare  earths 
is  three,  it  has  been  thought  best  to  show  them  on  the  vertical  rod  which 
represents  this  valence,  in  order  to  make  the  figure  as  simple  as  possible. 
Thus,  the  rare  earths  belong  in  a sense  to  the  third  group,  but  bear  a some- 
what peculiar  relationship  to  the  other  elements  of  the  group. 

Supposed  Imperfections  of  the  Periodic  System. 

A great  deal  of  attention  has  been  given  in  papers  in  journals,  and  in 
books,  to  what  have  been  called  the  imperfections  in  the  periodic  system. 
Among  the  most  emphasized  of  these  has  been  the  fact  that  when  ar- 
ranged in  a periodic  table  in  the  order  of  their  properties,  a few  elements, 
argon,  cobalt,  and  tellurium,  are  not  in  the  strict  order  of  their  atomic 
weights.  It  has  now  been  shown  by  Moseley  that  the  elements  in  the 
periodic  system  are  not  plotted  according  to  the  order  of  their  atomic  weights , 
but  according  to  the  order  of  their  X-ray  spectra , or  what  is  called  the  atomic 
number.  According  to  a theory  developed  by  Rutherford,  the  atomic 
number  represents  the  number  of  positive  charges  on  the  nucleus  of  the 
atom.  If  this  is  true  THE  periodic  system  shows  The  relation  BE- 
TWEEN THE  PROPERTIES  OF  THE  ELEMENTS  AND  THE  NUCLEAR  CHARGE  OF 
THE  ATOMS.  AND  THIS  IS  PRESUMABLY  EQUAL  TO  THE  NUMBER  OF  NEGATIVE 

Electrons  external  to  the  nucleus.  It  is  probably  the  spacing  and 
arrangement  of  these  external  electrons  which  determines  the  chemical  properties 

1 In  this  decrease  of  basic  properties  with  increase  in  atomic  weight  inside  one 
group  the  rare  earths  act  in  the  same  way  as  the  elements  on  the  front  of  the  inner 
loop,  and  it  is  quite  possible  that  it  is  better  to  state  the  fact  thus  than  to  give  the  some- 
what involved  explanation  expressed  above. 


J 

c. 


14 


and  those  physical  properties  of  the  elements  which  are  not  functions  of  the 
nuclear  mass.  When  considered  in  this  way  it  is  apparent  that  there  remain 
no  imperfections  in  the  system  to  be  explained,  for  it  is  not  necessary 
that  the  mass  of  the  atom  shall  vary  just  as  the  nuclear  charge.  Neither 
is  it  to  be  supposed  that*  all  of  the  properties  of  the  atoms  should  vary 
according  to  the  same  function  of  this  charge. 

Explanation  of  Regularities  and  Irregularities  in  the  Atomic  Weight 

Relations. 

In  a recent  series  of  papers1  Harkins  and  Wilson  have  presented  a theory 
in  regard  to  the  formation  of  complex  from  simple  atoms,  which  may  be 
used  to  explain  some  of  the  remarkable  relations  in  the  atomic  weights, 
such  as  exist  in  one  of  the  triads  of  Dobereiner. 

At.  wt.  Difference. 


Lithium 6.94 

Sodium 23.00 

Potassium 39. 10 


16.06 
16 . 10 


In  addition  to  the  occurrence  of  the  difference  16  in  this  triad 
it  is  found  that  the  atomic  weights  of  six  of  the  eight  elements  of 
the  third  series  may  be  found  by  adding  16  to  the  atomic  weights  of 
the  elements  just  above  them.  Between  Series  3 and  4,  two  of  the 
differences  are  again  16,  and  five  amount  to  20.  The  greatest  common 
divisor  of  these  numbers  is  4,  and  this  is  assumed  to  mean  that  in  general 
the  differences  in  mass  between  the  atoms  of  any  one  group  in  the  periodic 
table  are  due  to  differences  in  the  number  of  helium  atoms,  of  mass  4, 
which  have  been  used  up  in  their  formation.  The  proof  of  this  system 
can  not  be  given  here,  but  can  be  found  in  the  papers  to  which  reference 
has  been  made. 

The  explanation  of  these  regularities  is  made  more  apparent  by  Table  II. 

The  explanation  for  the  irregularities  in  the  atomic  weights  may  be  il- 
lustrated by  citing  the  case  of  argon,  which  has  an  atomic  weight  greater 
than  potassium,  which  comes  just  after  it.  This  irregularity  is  due  to 
the  tendency  for  the  atoms  as  they  grow  larger  to  take  on  helium  units 
more  rapidly.  If  argon  followed  the  rule  of  aggregation  as  followed  in 
Series  2,  its  mass  would  be  36,  but  the  tendency  to  take  on  helium  atoms 
more  rapidly  characterizes  Series  4.  The  elements  of  the  third  series 
are  formed  from  those  of  the  second  by  the  addition  of  four  helium  units, 
but  this  difference  grows  to  five  helium  units  between  Series  3 and  4. 

, Thus  from  neon  to  argon  is  5 helium  units  or  20,  and  20  + 20  gives  40, 
the  atomic  weight  of  argon.  Only  in  the  cases  of  potassium  and  calcium 
does  the  increment  between  the  series  fall  back  to  that  between  the  sec- 


1 J.  Am.  Chem.  Soc.,  37,  1367-96  (1915);  Phil-  Mag.,  30,  723-34  (1915)- 


i5 


Table  II. — A Periodic  System  Representing  in  General  the  System  Accord- 


ING  TO  WHICH  THE  ElEMEMTS  HAVE  BEEN  BUILT  Up 

FROM 

Hydrogen  . 

and  Helium. 

H detd. 

= 1.0078. 

Group. 

0. 

1. 

2. 

3.  4. 

5. 

6. 

7. 

8 

Series  2. 

He 

Li 

Be 

B C 

N 

O 

F 

He 

He+Hj. 

2He+H.  2He+H3.  3He.  3He+2H. 

4He. 

4He+H3. 

Calc 

. =h4 

7 

9 

II  12 

14 

16 

19 

Detd . . . 

• 4 

6.94 

9-i 

II  12 

14.OI 

16 

19 

Series  3. 

Ne 

Na 

Mg 

A1  Si 

P 

S 

Cl 

5He. 

5He+Ha. 

6He. 

6He+H3.  7He.  7He+H3. 

8He. 

8He+H3. 

Calc 

. 20 

23 

24 

27  28 

31 

32 

35 

Detd . . . 

. 20 

23 

24-3 

27.I  28.3 

31  .02 

32  -07 

35-46 

Series  4. 

A 

K 

Ca 

Sc  Ti 

V 

Cr 

Mn 

Fe 

Co 

lOHe. 

9He+H3. 

lOHe. 

1 lHe.  12He. 

12He+H3. 

13He. 

13He+H3. 

1 3He. 

14He+H3. 

Calc.... 

. 40 

39 

40 

00 

4" 

51 

52 

55 

56 

59 

Detd . . . 

. 39-88 

39-1 

40.07 

44.1  48.1 

51 

52 

54-93 

55.84 

58.97 

Increment  from  Series  2 to  Series  3=4  He. 

Increment  from  Series  3 to  Series  4=5  He.  (For  K and  Ca  = 4 He.) 
Increment  from  Series  4 to  Series  5=6  He. 


ond  and  third  series,  that  is  to  4 times  4 or  16.  In  other  words,  potas- 
sium has  the  atomic  weight  which  it  should  have  according  to  the  rule 
that  the  atomic  weight  increases  four  units  for  each  increase  of  two  in 
the  atomic  number.  Argon  has  a weight  four  more  than  this,  due  to  the 
taking  on  of  one  too  many  helium  units,  which,  however,  is  what  all  of 
the  fourth  series  elements  do  except  potassium  and  calcium. 

The  Radioactive  Elements. 

The  periodic  table  presented  in  this  paper  is  admirably  adapted  to  show 
the  relations  existing  between  the  radioactive  elements  as  expressed  by 
the  rule  of  Soddy  and  Fajans.  These  relations  are  expressed  on  the  space 
model  (Fig.  3),  and  better  still,  on  a space  model  on  which  the  vertical 
scale  is  made  much  greater,  for  example,  four  centimeters  to  one  unit 
of  atomic  weight.  Fig.  4 gives  an  enlarged  view  of  the  bottom  part 
of  the  table  shown  in  Fig.  3,  and  shows  the  elements  from  tantalum  to 
uranium.  In  this  figure  the  elements  derived  from  thorium  by  disintegra- 
tion are  designated  by  rectangles,  and  the  members  of  the  radium  series, 
by  sections  of  circles.  The  actinium  series  has  not  been  included,  since 
the  atomic  weights  are  not  known,  but  they  can  easily  be  added  as  soon 
as  the  atomic  weight  of  actinium  is  determined.  This  series  has  been  in- 
cluded in  Fig.  5 but  the  scheme  is  doubtful  so  far  as  the  actinium 
series  is  concerned. 

Uranium  (atomic  weight  238.2),  the  parent  of  the  members  of  the 
radium  series,  belongs  to  Group  VIB  on  the  back  of  the  inner  loop.  It 
shoots  off  an  alpha  particle  (the  doubly  positively  charged  nucleus  of  a 
helium  atom)  and  changes  into  uranium  Xi  (at.  wt.  234.2),  which  belongs 
to  Group  IVA.  This  gives  off  a beta  particle  and  changes  into  uranium 


i6 


Fig.  3- 


17 


Fig.  4. — Periodic  system  showing  the  radioactive  elements  of  the  thorium  and  radium 


series. 


i8 


£ 


5- — Table  of  the  radioactive  elements.  Note:  A new  determination  of  the  atomic  weight  of  thorium  gives  232.2, 
so  the  decimal  in  the  thorium  series  should  be  0.2.  The  actinium  series  is  not  yet  fixed  with  any  certainty. 


19 


i 


X2  (Group  VB)  without  a change  of  atomic  weight.  A second  beta  change 
converts  uranium  X2  into  uranium2,  isotopic  with  uranium  and  with  an 
atomic  weight  four  less.  This  is  converted  into  ionium  by  an  alpha 


Table  III. — Periods  of  the  Radioactive  Elements,  with  Isotopes  Classed 

Together. 


At. 

Name  of 

Atomic 

No. 

Isotopes  of 

isotope. 

weight.  Ray. 

Period. 

92 

Uranium 

Uranium2 

234-2 

a 

2 million  years 

Uranium 

238.2 

a 

5 billion  years 

91 

Uranium  X2 

Uranium  X2 

234.2 

0 

1 . 1 5 minutes 

90 

Thorium 

Radiothorium 

228 . 2 

a 

2 . 02  years 

Ionium 

230.2 

a 

200,000  years 

Thorium 

232 . 2 

a 

18  billion  years 

Uranium  Xi 

234.2 

a 

24.6  days 

Radioactinium 

. . . 

a, (3 

19.5  days 

Uranium  Y 

• . . 

1 . 5 days 

89 

Actinium 

Meso-thorium  2 

228 . 2 

0 

6.2  hours 

Actinium 

. . . 

. ... 

88 

Radium 

Thorium  X 

224.2 

a 

3 . 64  days 

Radium 

226 . 2 

a 

1730  years 

Meso-thorium  1 

228 . 2 

a 

5 . 5 years 

Actinium  X 

. • . 

1 1 . 4 days 

87 

(Unknown) 

86 

Niton 

Thorium  emanation 

220 

a 

54  seconds 

Radium  emanation 

222 

a 

3 . 85  days 

Actinium  emanation 

. . - 

a 

3 . 9 seconds 

85 

Unknown 

84 

Polonium 

Radium  F 

210 

a 

136  days 

Thorium  C' 

212 

a 

io-11  seconds 

Radium  C' 

214 

a 

io“6  seconds 

Thorium  A 

2l6 

a 

0.14  second 

Radium  A 

2l8 

a 

3 minutes 

Actinium  A 

a 

0.002  second 

Actinium  C' 

81 

Thallium 

Thorium  D 

208 

0 

3 . 1 minutes 

Radium  C2 

210 

0 

1 . 4 minutes 

Actinium  D 

• • • 

0 

4.71  minutes 

Thallium 

204 

Extremely  long 

83 

Bismuth 

Radium  E 

210 

0 

5 days 

Thorium  C 

212 

a,0 

60  minutes 

Radium  C 

214 

a,0 

19.5  minutes 

Actinium  C 

• • . 

a 

2.15  minutes 

Bismuth 

208 

• . . 

82 

Lead 

Lead  from  Ra 

206 

• • • 

Extremely  long 

Lead  from  Th 

208 

• • . 

Extremely  long 

Lead  from  actinium 

• • • 

Radium  D 

210 

0 

16.5  years 

Thorium  B 

212 

0 

10.6  hours 

Radium  B 

214 

0 

26.7  minutes 

Actinium  B 

• . • 

0 

36.1  minutes 

Lead  from  secondary  branch  of  radium  series 
Lead  from  secondary  branch  of  actinium  series 
Lead  from  secondary  branch  of  thorium  series 


/ 

\ 


> 8 


\ 


\ 


20 


change,  and  this  in  turn  changes  into  radium  by  another  alpha  transforma- 
tion. These  changes,  and  the  others  until  the  disintegration  ends  with 
lead  from  radium  (Pb  Ra),  can  be  easily  traced  by  following  the  lines 
in  the  table.  In  each  loss  of  an  alpha  particle  the  atomic  weight  de- 
creases by  approximately  four,  and  the  valence  and  group  number  both 
decrease  by  two.  Each  loss  of  a beta  particle  increases  the  valence  and 
group  number  by  one,  but  causes  no  change  of  atomic  weight. 

The  half-period  of  a radioactive  element  is  the  time  in  which  one-half 
of  the  element  would  disintegrate.  The  half-periods  of  each  set  of  isotopes 
are  given  in  Table  III. 

The  table  giving  the  periods  of  the  radioactive  elements  shows  that  the 
period  for  any  one  isotope  varies  with  the  atomic  weight  in  some  regular 
way.  It  is  difficult  to  make  any  comparison  in  this  sense  which  includes 
the  members  of  the  actinium  series,  since  their  atomic  weights  are  un- 
known. In  the  case  of  the  isotopes  of  thorium,  thorium  itself  has  the 
longest  period,  and  thus  decreases  in  each  direction  as  the  atomic  weight 
decreases  or  increases.  The  periods  of  the  isotopes  of  lead  decrease  as 
the  atomic  weight  increases,  and  the  same  is  true  of  the  periods  of  bis- 
muth and  its  isotopes.  However,  in  the  case  of  the  isotopes  of  polonium 
(Radium  F),  Thorium  C'  has  the  minimum  period,  and  the  period  in- 
creases on  .each  side  as  the  atomic  weight  either  increases  or  decreases. 

The  Nature  of  Isotopes. 

It  is  now  known,1  as  has  already  been  pointed  out,  that  a single  ele- 
ment, with  a single  atomic  number,  may  consist  of  several  different  kinds 
of  atoms,  which  are  alike  in  that  they  seem  to  have  the  same  nuclear 
charge,  and  therefore  presumably,  the  same  number  of  external  nega- 
tive electrons.  Isotopes  seem  to  be  identical  chemically,  and  so  far  as 
is  known  they  give  identically  the  same  spectrum,  but  they  may  or  may 
not  differ  in  certain  physical  properties,  such  as  the  melting  points.  Thus 
neon  and  meta-neon,  which  differ  in  atomic  weight  by  twTo,  were  separated 
by  diffusion.  On  the  other  hand,  Soddy  finds  that  lead  from  thorium  and 
ordinary  lead  have  the  same  atomic  volume,  that  is,  the  lead  obtained 
from  thorium  minerals  is  denser  than  ordinary  lead  in  the  ratio  of  the 
atomic  weights.  Richards2  has  found  that  the  lead  from  radium  is  also 
different  in  density  from  ordinary  lead.  Such  isotopes  as  these  differ 
in  those  properties  which  are  functions  of  the  mass  of  the  particle, 
and  they  may  be  called  isotopes  of  the  first  class.  A second  kind  of  iso- 
topism  is  that  in  which  there  is  no  difference  in  mass  except  that  due 
to  a difference  in  the  packing  effect.  Thus  Radium  D and  the  end  num- 
ber of  the  secondary  radium  disintegration  series,  which  is  as  yet  un- 
named, have  the  same  atomic  weight  except  for  the  very  slight  difference 

1 Le  Radium,  io,  17 1. 

2 J.  Am.  Chem.  Soc.,  38,  221  (1916). 


21 


in  mass  due  to  a difference  in  the  internal  energy  of  the  atoms,  and  this 
difference  is  so  slight  as  to  be  experimentally  undetectable,  so  these  may 
be  called  isotopes  of  equal  mass.  Also,  though  the  atomic  weight  of 
actinium  has  not  been  determined  as  yet,  enough  is  known  of  its  disin- 
tegration series  so  that  it  is  practically  certain  that  a number  of  actin- 
ium derivatives  show  this  form  of  isotopism  with  members  of  the  radium 
series.  Thus  if  we  assume  that  the  atomic  weight  of  actinium  is  230, 
then  radio-actinium  and  ionium  which  are  isotopic  must  both  have  atomic 
weights  of  230,  but  the  latter  has  a half-period  of  200,000  years,  and  the 
former  of  only  19.5  days,  so  there  is  a very  great  difference  in  stability. 
Even  if  the  atomic  weight  of  actinium  is  different,  it  will  be  seen  from 
Fig.  5 that  some  of  the  other  members  of  the  two  series  must  show 
this  form  of  isotopism. 

Isotopes  of  approximately  equal  atomic  mass  are  derived  from  the  same 
ancestral  atom,  that  is  from  either  uranium  or  thorium,  for  no  thorium 
disintegration  product  is  known  which  has  the  same  mass  as  a uranium 
disintegration  product.  In  the  formation  of  isotopes  of  this  class,  differ- 
ent amounts  of  energy  seem  to  be  given  out,  so  they  must  differ  in  internal 
energy,  and  to  a greater  or  lesser  extent  in  stability.  It  does  not  seem 
improbable  that  this  difference  may  be  due  to  the  expulsion  in  the  differ- 
ent cases  of  alpha  and  beta  particles  which  lie  in  structurally  different 
positions  in  the  nucleus. 

The  Nuclei  of  Complex  Atoms. 

, According  to  the  above  views,  and  those  advanced  by  Harkins  and 
Wilson  in  the  first  four  papers  of  this  series,  which  advanced  the  theory 
that  the  nuclei  of  complex  atoms  are  built  up  from  hydrogen  and  helium 
nuclei  according  to  the  system  presented  in  Table  II,  it  may  be  assumed 
that  the  chemical  nature  of  the  atom  is  independent  of  the  number  of 
particles  present  in  the  nucleus  of  the  atom,  and  therefore  of  the  mass 
of  the  atom,  and  is  also  independent  of  the  structure  of  the  nucleus,  so 
long  as  the  structure  does  not  affect  the  nuclear  charge.  The  chemical 
properties  of  the  atom  are,  according  to  this  view,  dependent  wholly 
upon  the  nuclear  charge.  When  the  complex  nucleus  is  built  up  from 
only  a few  hydrogen  and  helium  nuclei,  there  are  not  many  stable  ar- 
rangements which  give  a single  nuclear  charge,  but  when  the  nuclei  are 
very  complex,  the  possible  number  of  more  or  less  stable  structures  should 
be  considerably  increased.  Therefore  it  is  to  be  expected,  as  was  found 
by  Harkins  and  Wilson,  that  the  atomic  weights  of  the  lighter  elements 
should  follow  some  regular  system  with  only  small  deviations,  but  that 
these  deviations  should  become  much  more  considerable  in  the  case  of 
the  more  complex  heavier  elements.  In  other  words,  isotopes  should  be 
found  much  more  abundantly  among  the  heavy  than  among  the  light 
elements.  The  fact  that  the  isotopes  of  any  two  different  series  differ 


« 


22 


in  atomic  weight  by  about  two  units,  suggests  that  the  difference  is  caused 
by  the  presence  of  two  hydrogen  atoms  in  one  set  of  atoms,  and  their  ab- 
sence from  the  other.  As  examples  it  may  be  remembered  that  neon 
and  meta-neon  are  supposed  to  differ  in  atomic  weight  by  two  units,  and 
within  the  accuracy  to  which  the  atomic  weight  of  thorium  has  been  de- 
termined, there  is  the  same  difference  between  two  adjacent  isotopes  of 
the  thorium  and  the  uranium  series. 

A Plane  or  Spiral  Form  of  the  Periodic  Table. 

The  periodic  table  presented  in  this  paper  is  a space  form,  though  it 
is  easily  represented  on  a plane  as  in  Fig.  2.  The  space  form  may, 
however,  be  easily  converted  into  a plane  diagram  by  plotting  the  atomic 
weights  radially  from  a point  in  a plane.  This  gives  the  table  represented 
in  Fig.  6.  While  this  spiral  form  of  table  does  not  seem  to  the  writers 
to  be  so  well  adapted  to  general  use  as  the  space  form,  it  does  show  ex- 
actly the  same  relations  between  all  of  the  chemical  and  physical  proper- 
ties of  the  elements.1  This  table  is  different,  too,  from  other  spiral  tables, 
for  none  of  the  earlier  tables  have  been  so  constructed  as  to  classify  the 
elements  correctly.  Thus,  for  example,  the  spiral  table  given  in  Erd- 
mann’s chemistry  classifies  Ne,  Ni,  Rh,  and  Ir,  in  one  group,  Na,  Cu, 
Ag,  Gd,  and  Au  in  another,  and  Li,  K,  Rb,  Cs,  leaving  out  Na,  in  a third. 
These  are  obviously  improper  classifications.  The  error  in  all  previous 
spiral  tables  has  been  due  to  a failure  in  plotting  to  distinguish  between 
the  long  and  the  short  periods.  In  Fig.  7 the  short-period  elements 
occur  only  above  the  median  line,  while  the  long  periods  make  a contin- 
uous line  both  above  and  below. 

It  is  interesting  to  note  that  around  the  long  periods  the  group  num- 
bers run  o,  iA,  2A,  3A,  4A,  5B,  6B,  7B,  8,  iB,  2B,  3B,  4B,  5A,  6A,  7A,  o, 
which  is  exactly  the  order  in  the  tables  presented  in  Figs.  2 and  4. 
Table  7 is  the  first  spiral  table  to  give  the  chemical  relations  correctly. 

The  Relation  between  the  New  Form  of  the  Periodic  Table  and  the 

other  Modifications. 

In  his  book  entitled  “New  Ideas  on  Inorganic  Chemistry,”  Werner,2 
in  discussing  the  periodic  system,  says: 

“. , . . up  to  the  present  the  satisfactory  grouping  of  the  iron  group  and  the  rare 
earths  appears  to  be  almost  impossible.  Most  of  these  difficulties  are  not  difficulties 
of  principle,  i.  e.,  they  are  not  to  be  referred  to  the  nature  of  the  metal  in  question, 
but  rather  to  the  particular  arrangement  adopted  to  illustrate  the  periodic  occurrence 
of  chemically  allied  elements. 

“The  principle  chosen  by  Mendeleeff,  of  bringing  analogous  elements  as  near  as 
possible  together  in  order  to  bring  out  the  less  evident  similarities  which  exist  between 
such  elements,  has  been  followed  by  his  successors.  This  process  has  led  to  a crowding 

1 Except  that  it  does  not  show  so  well  the  relations  between  what  have  been  called 
complementary  groups. 

2 English  edition,  Longmans,  1911,  p.  4. 


23 


Fig.  6. — A spiral  form  of  the  periodic  table. 


24 


together  (Ineinanderschachtelung)  of  the  elements  which  is  harmful  to  the  synoptical 
character  of  the  periodic  system,  and  this  is  especially  true  when  we  consider  only  the 
less  important  analogies:  the  result  of  equal  valencies.  This  compression  of  the  ele- 
ments into  the  least  possible  space  is  the  chief  cause  of  many  elements  not  finding  a 
suitable  position  in  Mendeleeff ’s  scheme.  This  remark  is  particularly  applicable  to  the 
eighth  group,  and  to  the  metals  of  the  rare  earths.” 

However,  in  finding  a remedy  for  the  defects  which  he  discusses,  Werner 
goes  to  the  opposite  extreme,  and  places  the  elements  in  such  a way  that 
many  important  analogies  become  obscured.  By  placing  the  elements 
farther  apart  on  the  helix,  but  close  together  in  space,  the  new  table  is 
able  to  combine  all  of  the  advantages,  and  to  eliminate  the  disadvantages 
of  such  widely  different  forms.  The  relation  between  these  different 
tables  is  discussed  below. 

If,  in  Figs,  t,  2,  or  3,  the  lines  of  the  helix  are  cut  between  the  seventh 
and  the  zero  groups,  and  between  the  eighth  and  the  iB  groups,  the  table 
when  spread  out  on  a plane  becomes  much  like  that  of  Mendeleeff,  except 
that  there  are  no  blanks  except  those  which  correspond  to  atomic  numbers, 
that  the  rare  earths  are  arranged  differently,  and  that  the  drawing  would 
still  show  the  distinction  between  the  main  and  the  sub-groups.  How- 
ever, if  all  of  the  connecting  lines  are  taken  out,  the  table  becomes  es- 
sentially that  of  Mendeleeff.  If  the  helix  is  cut  only  between  the  seventh 
and  the  zero  groups,  unrolled,  and  laid  on  a plane,  it  takes  on  the  general 
form  of  the  Carnelley-Richards  table,1  which  is  probably  the  best  of  all 
of  the  plane  tables  except  that  of  Mendeleeff.  If  the  helix  is  cut  between 
carbon  and  nitrogen,  between  silicon  and  phosphorus,  and  between  the 
seventh  and  the  zero  groups,  and  again  spread  on  a plane,  it  gives  the  form 
attributed  to  Meyer,  to  Palmer,  and  to  Staigmuller.2  The  essential  ad- 
vantage claimed  by  Staigmuller  is  that  in  his  table  a line  separating  the 
non-metals  and  the  metals  may  be  easily  drawn,  and  that  the  non-metals 
fall  into  one  group  in  the  table.  The  elements  which  he  classifies  as  non- 
metals  are  B,  C and  Si,  N,  P (and  partially  As) ; O,  S,  Se  (and  partly  Te) ; 
F,  Cl,  Br,  and  I;  and  also  He,  Ne,  A,  Kr,  and  Xe.  If  this  is  an  advantage 
of  the  Staigmuller  table,  it  is  much  more  an  advantage  of  the  new  space 
form  here  presented,  as  in  our  table  the  non-metals  are  much  more 
closely  grouped,  as  they  lie  entirely  in  one  group  on  the  outer  cylinder, 
and  all  except  B,  C and  Si,  lie  at  the  back. 

Werner’s  table,3  except  for  the  arrangement  of  the  rare  earths,  may  be 
obtained  by  cutting  the  helix  so  that  the  elements  in  each  of  the  following 
pairs  of  elements  become  separated:  Li  and  Be,  Na  and  Mg,  Ca  and  Sc, 
Sr  and  Y.  It  should  also  be  cut  between  the  o and  iA  groups,  and  then 
spread  out  on  a plane.  The  transformation  into  the  form  devised  by 

1 Chem.  News,  78,  193-5  (1898). 

* Nernst’s  “Theoretische  Chemie,”  Siebente  Auflage,  p.  184. 

3 Ibid.,  p.  185. 


25 


Walker1  is  also  a simple  one,  since  the  spiral  needs  only  to  be  cut  between 
the  seventh  and  zero  groups,  and  the  vertical  rods  severed  between  K 
and  Rb,  between  Ca  and  Sr,  Sc  and  Y,  Si  and  Ti,  P and  V,  S and  Cr,  and 
between  Cl  and  Mn. 

As  has  already  been  seen,  the  new  table  may  be  represented  on  a plane 
as  a spiral,  or  in  space  as  a figure  8.  The  use  of  a figure  8 space  form  of 
table  was  first  suggested  by  Crookes,2  but  the  arrangement  of  the 
elements  in  his  table  was  very  different.  The  use  of  a figure  8 dia- 
gram has  been  advocated  by  Soddy,3  who  gives  the  best  table  previously 
devised  but  such  a representation  obscures  both  what  have  been  called 
the  complementary  relations  and  the  relations  between  the  main  and  the 
sub-groups. 

While  in  the  development  of  the  periodic  table  in  space  as  presented 
in  this  paper,  no  use  was  made  of  any  previously  devised  system  except 
that  of  Mendeleeff,  it  will  be  seen  that  it  is  a generalized  form,  of  which 
the  Mendeleeff,  Carnelley-Richards,  Werner,  Staigmiiller,  and  other  modi- 
fications, are  special  cases,  each  of  which  expresses  certain  relations  well, 
but  others  poorly  or  not  at  all.  The  space  form  eliminates  the  disadvan- 
tages of  the  different  plane  tables,  and  at  the  same  time  combines  their 
advantages.  That  at  first  sight  it  seems  more  complex  than  the  Mendel- 
£eff  table  is  due  to  the  fact  that  it  classifies  all  of  the  elements,  but  it  is 
actually  more  simple,  since  it  contains  no  blanks  except  the  five  which 
correspond  to  atomic  numbers.  Experience  has  shown  that  students 
who  have  no  previous  knowledge  of  the  Mendeleeff  table  find  the  space 
form  the  more  simple,  at  least  when  they  have  the  model  to  use  in  their 
study. 

COHESIONAL  PROPERTIES. 

Atomic  Volumes,  Melting  Points,  and  Related  Properties. 

In  Fig.  i the  elements  of  highest  atomic  volume  lie  at  the  left  of  the 
outer  loop,  while  the  elements  of  lowest  atomic  volume  lie  at  its  right 
(carbon,  silicon  and  aluminium)  as  long  as  the  outer  loop  persists  at  the  ex- 
treme right,  and  when  the  outer  loop  disappears  at  this  extremity,  the  line 
of  lowest  atomic  volume  jumps  over  to  the  left  end  of  the  inner  loop.  To 
show  these  atomic  volume  relations  somewhat  more  simply  the  table  has 
been  drawn  in  the  form  given  in  Fig.  7.  From  the  standpoint  of  the  chemical 
relations  this  latter  table  is  much  less  perfect  than  the  former,  but  it  has 
the  one  advantage  that  the  elements  of  high  atomic  volume  are  at  the  left 
of  the  table,  and  those  of  low  atomic  volume  are  at  the  right,  so  if  this 
table  is  hung  with  its  left  side  as  the  top,  the  loops  take  the  general  form  of 

1 Chem.  News,  63,  251-3  (1891). 

2 Ibid.,  78,  25  (1898);  Proc.  Roy.  Soc.,  63,  408-11  (1898);  and  Z.  anorg.  Chem., 
18,  72-6  (1898). 

3 Chemistry  of  the  Radioactive  Elements,”  Part  II,  p.  11. 


26 


r - 


40 


6C 


80 


100 


120 


140 


160 


180 


20C 


220 


240 
o H 

li 


GROUP/  0 


Fig.  7. — Periodic  table  modified  so  as  to  show  the  atomic  volume  relations  in  a simple  way. 


2 7 


the  atomic  volume  curve.1  Fig  7 has  the  great  disadvantage  that  it  does 
not  show  the  relations  which  exist  between  the  main  and  the  sub-groups. 
It  is  formed  from  the  table  in  Fig.  2 by  turning  each  inner  loop  on  a 
horizontal  axis  from  front  to  back  at  its  right  ends  until  it  falls  outside 
to  the  right.  The  atomic  volumes  of  the  elements  have  been  plotted 
against  their  atomic  numbers  in  Fig.  8.  A comparison  of  Figs,  i,  2, 
7 and  8 will  show  how  simply  the  present  form  of  table  expresses  the 
atomic  volume  relations. 

The  elements  of  lowest  melting  point  lie  at  the  left  of  the  table  (Figs. 
1,  2,  and  7).  The  absolute  melting  points  for  these  elements  are: 


Hydrogen 
Helium . . 
Neon. 

Argon 

Krypton . 

Xenon 

Niton 


14° 

_ O 


85° 
104  0 
1 33° 
202  0 


The  line2  of  highest  melting  points  begins  exactly  opposite  at  the  right 
of  the  outer  loop  with  carbon,  melting  point  about  3900 0 absolute,  and 
silicon,  1693°.  These  are  the  elements  of  lowest  atomic  volume  except  for 
the  fact  that  the  atomic  volume  of  aluminium  is  slightly  less  than  that  of 
silicon.  It  might  seem  that  the  line  of  maximum  melting  point  would  here 
jump  at  once  to  the  elements  of  lowest  atomic  volume  in  the  next  series,  that 
is,  to  the  iron  group.  Instead  of  doing  this,  however,  it  passes  to  titanium 
(m.  p.  2060°  Abs.),  and  then  still  further  toward  the  eighth  group,  but 
reaches  only  to  Group  VIB,  and  passes  straight  down  through  molyb- 
denum (2800°),  tungsten  (3300 °),  and  uranium.  The  tendency  toward 
the  shift  of  the  maximum  melting  point  from  the  fourth  group  to  Group 
VIB  is  already  seen  in  the  elements  titanium  and  vanadium.  Thus  the 
difference  between  the  melting  points  of  carbon  (4th  group)  and  the  adja- 
cent element  in  the  fifth  group,  nitrogen,  is  3800°.  Between  silicon  and 
phosphorus  the  corresponding  drop  is  1400°.  Just  below  this  the  drop 
from  titanium  (4th  group)  to  vanadium  (Group  VB)  is  only  70  °.  This 
enormous  decrease  in  the  fall  between  the  fourth  and  fifth  groups,  clearly 
predicts  a reversal  in  the  next  series,  where  zirconium  (4th  group)  has  a 
melting  point  of  about  2000 0 absolute.  Columbium  (niobium,  5th  group) 
melts  at  2500 °,  and  molybdenum  (Group  VIB)  melts  at  about  2800°. 

1 If  the  loops  at  right,  representing  the  sub-groups,  are  untwisted,  this  table  takes 
on  the  form  advocated  by  Emerson  in  his  “Helix  Chemica,”  Am.  Chem.  J 45,  160-210 
( 1 9 1 1 ),  except  that  the  new  table  classifies  the  rare  earths  in  a different  way.  While  this 
is  also  a useful  form  of  the  table,  it  has  not  been  thought  necessary  to  include  a 
figure  showing  it,  since  it  is  easy  to  see  how  Emerson’s  table  can  be  modified  so  as  to 
classify  the  rare  earths  correctly. 

2 For  the  lines  of  maximum  melting  points,  and  the  lines  of  primary  and  secondary 
minima,  see  Fig.  9. 


28 


29 


MELTING  POINTS 
Line  of 
Line  of 
Line  of 


Primary  Minima—... 
Secondary  Minima— 

Fig.  9 


Table  IV. — The  Elements  Arranged  According  to  Atomic  Numbers,  with  the  Atomic  Weights,  Atomic  Volumes,  Melting 
Points,  Compressibilities,  Cubic  Coefficients  of  Expansion,  Magnetic  Susceptibilities,  Atomic  Frequencies,  and 

Values  of  T™/V  Representing  Cohesion. 


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Table  IV  ( continued ). 

Compressibility  Suscep-  Atomic 

At.  At.  Cubic  coeffs.  of  M.  p.  at  20°  X 1 0«.  tibility  frequency 

Element.  wt.  vol.  Density.  expansion  3a  X 106.  absolute.  (Richards.)  X 107.  X 1 012.  Tm/V. 


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34 


The  unknown  element  eka-manganese  2 may  prove  to  have  a higher 
melting  point  than  tungsten.  The  drop  in  melting  point  between  car- 
bon, atomic  number  6,  and  nitrogen,  atomic  number  7,  is  the  most  re- 
markable sharp  change  in  the  whole  system,  amounting  as  it  does  to  more 
than  3800°.  It  will  be  shown  later  that  the  relations  of  the  physical 
properties  of  carbon  to  those  of  the  other  elements,  are  remarkable  in 
many  other  respects. 

In  addition  to  the  line  of  minimum  melting  points,  which  lies  in  the 
zero  group,  there  is  a line  of  secondary  minima,  possibly  beginning  with 
aluminium,  with  a very  slight  minimum.  The  next  element  in  the  third 
group  below  this  is  scandium,  and  unfortunately  its  melting  point  is  not 
known.  Below  this  in  Group  IIIA  there  is  a very  considerable  minimum 
beginning  with  gallium  (at.  no.  31)  of  absolute  melting  point  303  °,  while 
just  before  it  zinc  (at.  no.  30)  has  a melting  point  of  692°,  and  just  after 
it  comes  germanium  (at.  no.  32)  with  a melting  point  of  12310.  Below 
gallium  the  minimum  continues  in  the  same  group,  IIIB,  with  indium 
(m.  p.  480°),  and  then  shifts  to  the  left  (Fig.  9)  toward  the  iron  group, 
so  that  the  next  minimum  comes  in  Group  IIB  with  mercury.  Here  it  is 
remarkable  that  the  secondary  minimum  where  mercury  melts  at  234 0 
absolute,  is  almost  as  low  as  the  corresponding  primary  minimum  at 
niton,  which  melts  at  202  °,  or  only  32 0 lower.  It  will  be  seen  that  the 
line  of  maximum  melting  points  at  the  back  of  the  inner  loop,  and  the 
line  of  secondary  minima  at  the  front  of  the  inner  loop,  both  move  to  the 
left  toward  the  iron  group  as  they  move  down  the  table.  In  Fig.  8 
the  melting  points  have  been  plotted  as  reciprocals,  and  these  secondary 
minima  may  be  seen  as  secondary  maxima  on  the  curve. 

Fig.  8 is  similar  to  a figure  given  by  Richards,1  but  differs  in  the 
fact  that  it  is  plotted  to  atomic  numbers  instead  of  atomic  weights,  and 
also  gives  data  for  some  of  the  properties  of  as  many  as  72  elements, 
while  Richards’  figure  shows  only  38.  The  increase  in  the  number  of 
data  changes  not  only  the  form  of  individual  curves,  but  it  also  changes 
their  relationship  to  each  other.  When  so  many  data  are  plotted,  there 
is  a considerable  advantage  in  plotting  to  atomic  numbers  instead  of 
atomic  weights,  since  when  the  atomic  weights  are  plotted,  each  curve 
is  apt  to  cross  itself  whenever  the  atomic  weights  are  not  in  the  order 
of  the  atomic  numbers,  as  is  the  case  with  argon.  Another  point  in  favor 
of  plotting  these  physical  properties  according  to  the  atomic  numbers 
instead  of  atomic  weights,  is,  as  will  be  shown  later,  that  it  is  the  number 
of  external  electrons  in  the  atom,  and  the  number  of  these  runs  in 
the  same  order  as  the  atomic  numbers,  which,  in  all  probability,  deter- 
mines the  cohesional  properties  of  the  elements.  Moseley’s  work 
seems  to  indicate  that  the  atomic  number  and  the  nuclear  charge,  pre- 
1 J.  Am.  Chem.  Soc.,  37,  1649  (1915). 


35 


sumably  equal  to  the  number  of  external  electrons,  are  expressed  by  the 
same  number. 

The  data  on  compressibility  given  in  Table  IV,  and  plotted  in  Fig.  8, 
have  been  taken  from  Richards’  work,  and  the  other  data  were  obtained 
from  what  seemed  to  be  the  most  reliable  sources,  though  in  many  cases 
there  is  considerable  doubt  as  to  which  work  is  the  most  trustworthy. 
A few  of  the  data  plotted  have  been  taken  from  work  on  liquids,  but  wher- 
ever this  is  done  the  fact  is  specified  in  Table  IV.  A dotted  line  in  the 
figure  indicates  that  data  are  not  available  for  the  elements  along  the  line, 
while  an  unbroken  line  shows  that  no  data  have  been  omitted. 

The  four  curves  representing  the  reciprocals  of  absolute  melting  points, 
coefficients  of  expansion,  atomic  volumes,  and  compressibilities,  have  all 
the  same  form,  though  they  are  not  so  closely  similar  as  those  plotted  by 
Richards.  The  deviations  have  been  introduced  by  the  addition  of  more 
data.  The  two  curves  at  the  top,  giving  the  reciprocals  of  the  melting 
points  and  coefficients  of  expansion,1  are  almost  exactly  similar  where 
the  data  are  complete.  Thus  the  secondary  minima  in  the  melting 
points  have  corresponding  maxima  in  the  coefficients  of  expansion  for 
indium  and  mercury,  and  a maximum  may  be  predicted  for  gallium, 
though  no  determination  has  been  made  for  this  metal  The  atomic 
volume  curve  does  not  show  any  corresponding  maxima,  and  they  seem 
also  to  be  absent  from  the  compressibility  curve,  though  not  all  of  them 
are  known  in  the  latter  case. 

The  only  minimum  melting  point  which  exactly  corresponds  to  a max- 
imum atomic  volume,  is  that  for  helium.  Below  this  in  the  table  (Figs, 
i and  8),  the  maximum  atomic  volume  shifts  one  group  to  the  alkalies, 
while  the  minimum  melting  point  continues  to  remain  in  the  zero  group. 
In  a very  similar  way  carbon  is  the  only  element  of  minimum  atomic  vol- 
ume which  has  the  maximum  melting  point.  In  the  next  series  the  maxi- 
mum melting  point  again  comes  in  the  fourth  group  with  silicon,  but  the 
minimum  atomic  volume  has  shifted  one  group  to  aluminium  in  Group 
III.  In  the  next  period  molybdenum  has  the  highest  melting  point, 
but  the  element  of  lowest  atomic  volume  is  either  ruthenium  or  columbium, 
the  latter  if  the  density  used  is  correct,  but  as  to  this  there  seems  to  be 
considerable  doubt,  so  the  minimum  is  probably  at  ruthenium.  In  the 
next  period  osmium  has  the  lowest  atomic  volume,  while  tungsten  with 
an  atomic  number  two  less,  has  the  highest  melting  point. 

To  a considerable  extent,2  the  rule  holds  that  elements  of  low  charac- 
teristic valence  have  low  melting  points,  high  atomic  volumes,  high  eo- 

1 In  the  figure  this  curve  seems  to  have  much  flatter  maxima  than  the  one  above 
it,  but  this  is  mostly  due  to  the  fact  that  the  maxima,  which  lie  in  the  helium  group, 
are  omitted  from  this  curve  on  account  of  the  absence  of  data. 

2 This  is  not  a true,  but  only  an  apparent  relation,  as  is  shown  later. 


36 


efficients  of  expansion,  and  high  compressibility.  On  the  other  hand, 
to  the  same  extent,  elements  of  high  maximum  characteristic  valence 
have  low  atomic  volumes,  small  coefficients  of  expansion,  small  com- 
pressibilities, and  high  melting  points.  Blom1  has  calculated  a quantity, 
W,  which  he  finds  to  have  the  dimensions  of  a cohesion.  His  equation 
for  W is 

v2.A 

W = constant  — n- 
V /s 

where  v is  the  frequency  calculated  from  the  specific  heats,  A is  the  atomic 
weight,  and  V is  the  atomic  volume.  The  curve  for  log  W has  the  general 
form  of  the  melting  point  curve,  and  the  reciprocal  of  this  curve  would 
therefore  have  the  general  form  of  those  plotted  in  Fig.  6.  In  other 
words,  the  four  properties  plotted  in  Fig.  6 are  closely  related  to  the  co- 
hesion, or  it  may  be  considered  that  the  cohesion,  or  the  attraction  be- 

/ 

tween  the  particles,  conditions  all  of  the  other  four  properties.  The  point 
at  which  the  parallelism  between  valence  and  cohesion  meets  its  worst 
failure  is  in  the  case  of  the  sub-group  elements  such  as  copper  and  zinc, 
which  fall  just  beyond  the  eighth  group,  since  the  valence  of  these  elements 
is  low  and  their  cohesion  high.  Therefore  a better  rule  than  the  above  is 
that  in  Fig.  2 the  elements  at  the  ends  of  the  periods  He,  Ne,  A,  Kr, 
Xe,  Nt,  are  elements  of  high  atomic  volume,  high  coefficients  of  expansion, 
high  compressibilities,  low  cohesion,  and  low  melting  points,  while  the 
elements  at  the  middle  of  the  short  and  long  periods,  and  around  the  eighth 
group  near  the  middle  of  the  very  long  period,  are  in  general  the  elements 
of  high  cohesion  and  melting  points,  and  low  atomic  volumes,  compressi- 
bilities, and  coefficients  of  expansion. 

There  is  also,  as  might  be  expected,  a general  relation  between  the 
hardness  of  an  element  and  the  properties  under  discussion.  Thus,  the 
very  hard  elements  lie  near  the  middle  of  the  periods  while  the  softest 
elements  lie  near  the  ends  of  the  periods. 

From  the  above  considerations  it  seems  likely  that  the  apparent  connec- 
tion between  maximum  characteristic  valence  and  cohesion,  which  how- 
ever fails  so  badly  in  the  case  of  elements  of  low  valence  on  the  inner  loop, 
is  not  real,  but  that  the  cohesion  is  conditioned  by  the  spacing  of  all  the 
electrons  of  the  atom  external  to  the  nucleus,  and  that  this  spacing  is  a 
periodic  function  varying  in  the  periods  corresponding  to  those  given  in 
Fig.  2.  On  the  other  hand,  the  valence  varies  in  SERIES,  and  only 
partly  according  to  the  periods.  Thus  the  valences  1,  2,  3,  4,  5,  6,  7 
depend  only  on  the  position  in  the  series;  and  only  the  occurrence  of  the 
two  valences  o and  8 depends  upon  the  position  in  the  periods. 

It  seems  probable  that  the  atom  is  a system  consisting  of  a positive 
nucleus,  surrounded  by  one  or  more  negative  electrons  which  are  describing 
1 Ann.  Physik,  [4]  42,  1397-1416  (1913). 


37 


orbits  at  a high  speed.  It  is  not  improbable  that  the  force  which  keeps 
two  atoms  apart  is  due  to  the  repulsion  of  the  negative  electrons  of  one 
atom  for  those  of  the  other.  The  compression  of  a solid  would  bring 
these  atoms  closer  together  and  the  closer  approach  of  the  external 
electrons  would  rapidly  increase  the  repulsion.  The  principal  decrease 
in  volume,  is,  in  all  probability,  most  largely  due  to  the  decrease  in  dis- 
tance between  the  atoms.  When  such  large  pressures  as  those  used  by 
Bridgeman  are  used,  it  would  seem  likely  that  there  may  be  a considera- 
ble decrease  in  the  size  of  the  atoms  themselves.  That  the  atoms  are 
compressible  would  seem  almost  certain,  but  the  possibility  exists  that 
the  atoms  may  be  very  much  less  compressible  than  the  spaces  around 
them. 

The  Dimensions  of  Atoms. 

It  is  of  interest  in  this  connection  to  compare  what  are  often  called 
atomic  diameters,  but  which  are  more  properly  considered  as  the  distances 
between  the  centers  of  two  atoms  in  a gas  during  a collision,  as  determined 
from  the  kinetic  theory,  and  the  distances  between  the  centers  of  the  same 
atoms  in  their  positions  of  equilibrium  in  the  solid  or  liquid  state.  Such 
a comparison  is  given  in  Table  V. 

Table;  V. — Atomic  Diameters  or  Monatomic  Gases  (Distance  between  Atomic 
Centers  during  Collision)  as  Determined  from  the  Kinetic  Theory,  and 
the  Distances  between  the  Centers  of  the  Atoms  in  Liquids  or  Solids. 

Number  of  Atomic  diameter 


external  X 108  cm.  in  gases  Distance  X 108  cm.  between  cen- 
Substance.  electrons.  at  0°  C.  = D.  ters  of  atoms  in  solids  or  liquids.  T m/V. 

3.38  ( — 258°  adsorbed  in  charcoal) 

He 2 1.7  3-94  ( — 271. 50)  0.085 

Ne 10  2.1  3.17  (calc.)  ' 1.04 

A 18  2.5  3.56  (Liq., —189°)  3.0 

Xe 54  3.2  3.94  (Liq., — 1020)  3.6 

Molecular  Diameters  of  Diatomic  Gases. 

H2 2.1  3.12  ( — 252 °) 

N2 2.8  3-56  ( — 252 .5°,  solid) 

02 2.6  3-33  ( — 252 .5°,  solid) 


At  first  sight  it  might  seem  that  the  data  on  the  distance  between 
the  centers  of  the  atoms  in  gases  during  collisions  could  be  explained 
on  the  basis  that  the  lighter  atoms  approach  each  other  more  closely 
because  they  have  the  greater  velocities,  but  that  this  is  not  true  can  be 
seen  when  it  is  remembered  that  the  heavier  atoms  have  the  greater 
momentum,  so  the  closer  approach  of  the  lighter  atoms  of  the  helium 
group  is  due  to  the  fact  that  either  (i)  the  atoms  are  smaller,  or  (2)  that 
the  fields  of  force  around  them  are  less  intense  on  account  of  the  fact 
that  they  have  a smaller  number  of  electrons  external  to  the  nucleus 
(as  well  as  a higher  nuclear  charge).  Probably  each  of  these  factors 
plays  a part.  Thus  if  the  number  of  external  electrons  is  equal  to  the 


38 


nuclear  charge,  and  we  use  the  hypothesis  that  the  nuclear  charge  is  equal 
to  the  atomic  number,  then  it  might  reasonably  be  expected  that  the 
54  external  electrons  of  xenon  would  both  occupy  more  space,  and  create 
a more  intense  field  of  force  than  the  2 external  electrons  of  helium.  If 


the  number  of  external  electrons  is  indicated  by  N,  then 


atVs 

1NXe 

TVfVs 

iNJHe 


= 3»  so 


that  if  the  distances  between  the  centers  of  like  atoms  during  collision 
were  proportional  to  the  cube  root  of  the  number  of  external  electrons, 
then  since  this  distance  D is  1.7  for  helium  it  would  be  5.1  for  xenon, 
while  the  calculated  value  is  less  than  this,  or  3.2.  However,  the  momen- 
tum of  the  xenon  atom  is  5.7  that  of  the  helium  atom,  so  that  the  higher 
momentum  would  cause  the  atoms  to  approach  closer  than  a distance 
of  5.1,  but  it  is  doubtful  if  even  a momentum  5.7  times  as  great  would 
be  able  to  reduce  D to  3.2.  In  Table  VA,  values  are  given  for  different 
roots  of  N,  the  momentum,  and  the  calculated  values  of  D from  Table  V. 


Table;  VA . 

Relative 

Atom.  momentum.  D X 108  cm.1  &iNl/6.  feN  / <.  &3NV3.  N. 

He 1.0  1.7  1.7  1.7  1.7  2 

Ne 2.2  2.1  2.3  2.5  2.9  10 

A '.  3.15  2.5  2.6  2.9  3.5  18 

xe 5-7  3-2  3-3  3-9  5-i  54 


The  table  shows  that  the  distance  of  approach  D varies  quite  closely  as 
the  fifth  root  of  the  number  of  external  electrons  N.  If  all  of  the  atoms 
at  o°  had  the  same  momentum  this  might  be  thought  to  be  the  law  which 
conditions  their  approach,  but  since  the  momentum  increases  rapidly 
with  the  mass  of  the  atom,  it  is  probable  that  D would  vary  more  nearly 
as  the  fourth  or  third  root  if  the  momenta  were  the  same.  That  D is 
found  to  vary  as  the  fifth  root  of  N,  when  the  momentum  is  involved 
in  addition  to  the  number  of  external  electrons  N,  is  probably  due  to  the 
fact  that  the  momentum  is  a function  of  the  atomic  weight,  which  is  a 
function  of  the  atomic  number,  or  N,  in  this  case  the  number  of  charges 

1 The  values  of  D are  taken  from  Landolt-Bornstein-Meyerhoffer  Tabellen  and 

are  calculated  from  the  equation  D = ^ ° P°  , where  n is  the  number  of  mole- 

\ V 2 7TW  [JL 

cules  per  cc.  at  o°  and  760  mm.  Hg  = 2.705  X io19  cm.-3,  and  ju  is  the  viscosity  of  the 
gas,  with  the  application  of  Sutherland’s  correction  for  cohesional  force  {Phil.  Mag., 
I7>  320  (1904)),  and  Jean’s  correction  for  the  persistence  of  velocities.  The  constants 
involved  in  this  calculation  are  not  very  well  known,  and  may  vary  for  different  kinds 
of  atoms,  but  are  probably  the  same  for  atoms  of  the  same  kind,  such  as  those  of  the 
helium  group.  In  a table  prepared  by  the  General  Electric  Company  the  values  of 
D are  given  as  follows:  He  = 1.905,  A = 2.876,  and  these  numbers  are  in  the  same 
ratio  as  those  given  by  Landolt-Bomstcin.  On  account  of  the  uncertainty  in  the 
constants,  it  has  not  been  thought  worth  while  to  recalculate  the  numbers,  since  the 
relative  values  would  not  be  affected. 


39 


on  the  nucleus.  In  other  words  the  various  factors  involved  are  functions 
of  the  same  variable. 

If  the  heavier  helium  group  atoms  are  larger  it  may  seem  surprising 
that  in  the  liquid  state  the  distance  between  the  atomic  centers  is  practi- 
cally the  same,  but  this  is  due  to  the  fact,  as  is  shown  by  the  last  column 
in  Table  V,  that  the  cohesion  increases  very  rapidly  with  the  atomic 
number.  At  present  little  is  known  as  to  the  actual  dimensions  of  atoms, 
and  it  seems  probable  that  their  dimensions  are  smaller,  rather  than  larger 
than  those  usually  cited.  It  is  somewhat  difficult  to  know  what  is  meant 
by  the  atomic  diameter,  since  in  a simple  atom,  such  as  hydrogen,  it 
might  be  expected  that  the  diameters  would  be  very  different  in  the 
different  directions. 

In  the  calculation  the  number  of  gram  molecules  per  gram  molecular 
weight  was  taken  as  6.062  X io23.  According  to  the  table  the  centers 
^ of  the  atoms  in  liquids  or  solids  are  much  farther  apart  than  the  distance 
between  the  centers  in  gases  at  the  time  of  their  closest  approach  during 
collision.  Even  in  their  collisions  it  is  improbable  that  the  exterior  elec- 
trons come  very  closely  in  contact  in  comparison  with  their  dimensions. 
The  data  in  Table  V are  in  accord  with  the  usual  assumption  that  a large 
part  of  the  space  in  liquids  and  solids  is  outside  the  boundaries  of  the 
atoms,  though  the  interatomic  spaces  are  certainly  regions  in  which  the 
electro-static  and  electro-magnetic  forces  are  intense. 

Atomic  Frequencies. 

The  properties  of  the  elements  which  have  been  considered  thus  far  are 
properties  of  the  atoms  in  bulk,  undoubtedly  conditioned  however,  by 
the  structure  of  the  single  atoms.  An  endeavor  has  been  made  to  find  some 
property  which  is  more  characteristic  of  the  atoms  themselves.  This  at- 
tempt has  met  with  success  in  the  discovery  that  the  atoms  of  solid  sub- 
stances have  characteristic  atomic  frequencies.  While  in  the  simple 
theory  the  atomic  frequency  may  be  considered  as  independent  of  the 
nature  of  the  substance,  this  is  not  altogether  true,  since,  for  example, 
there  is  found  to  be  a difference  in  the  values  obtained  for  diamond  and 
graphite.  On  the  other  hand,  it  is  remarkable,  as  has  been  pointed  out 
by  Nernst,  that  the  frequencies  of  sodium  atoms  in  metallic  sodium  and 
in  sodium  chloride,  though  not  exactly,  are  approximately  the  same,  so 
as  a first  approximation  the  atomic  frequencies  may  be  considered  as  a 
property  of  the  atom. 

The  characteristic  equation  for  the  frequency  is  the  formula  for  the  sim- 
ple pendulum 


where  A is  the  atomic  weight,  and  D is  the  directional  force.  The  fre- 
quencies for  the  different  atoms  are  given  in  Table  II,  and  in  Fig.  10. 


40 


Atomic  Number  10  20  30  40  50  60  70  80  90  fOO 


4i 


However,  in  the  figure  the  reciprocals  of  the  frequencies  have  been  plotted 
instead  of  the  values  themselves,  since  the  change  makes  the  curve  com- 
parable with  those  representing  the  atomic  volumes,  compressibilities, 
coefficients  of  expansion,  and  reciprocals  of  the  melting  points,  as  plotted 
in  Fig.  8. 

The  different  equations  which  may  be  used  for  the  calculation  of  v 
have  been  discussed  by  Blom,1  who  has  compared  them  and  finds  that 
no  one  is  exclusively  better  than  the  others.  The  equations  are  given 
below,  where  the  symbols  have  the  following  meanings: 

Tw  = absolute  melting  point. 
d = density. 

V = atomic  weight. 

K = compressibility. 

a = linear  coefficient  of  expansion. 

C p and  Cv  — atomic  heats. 

1.  Einstein’s  equation.2 

yVs 

D = const.  — . 

K 

V = 3.3  X io7.A-1/,.(i-,/*.K-,/!. 

2.  Lindemann’s  equation,3  derived  from  the  hypothesis  that  at  the 
melting  point  the  orbits  of  the  atoms  become  just  large  enough  so  that 
the  atoms  come  into  direct  contact,  and  that  on  account  of  the  consequent 
energy  exchange  between  the  atoms,  they  are  no  longer  able  to  hold  to  their 
positions  relative  to  the  space  lattice,  but  begin  to  slide  past  each  other. 

T 

D = const.  — T7-. 

V2/3 

v = 31  X io12.  \l  ^ 2/. 

\ A.V  /a 


3.  Alterthum,4  from  dimensional  considerations,  found  the  following: 

1 


D = const. 


aV 


2/s 


v = 4.2  X 10 


11 


V 


AaV2/* 


4.  Benedicks5  considered  D as  proportional  to  the  internal  pressure 
of  the  solid  as  determined  by  van  der  Waal’s  equation. 

D = const.  -5-:. 

2>aV 

1 Ann.  Physik,  42,  1397-1416. 

2 Ibid.,  34,  170  (1911);  35,  679  (1911). 

3 Inaug.  diss.,  Berlin,  1911;  Physik.  Z.,  11,  609-12  (1910). 

4 Verh.  deutsch.  physik.  Ges.,  15,  68  (1913). 

6 Benedicks,  Ann.  Physik,  42,  154  (1913). 


5.  Griineisen’s1  equation: 


D = const. 


C„ 


v = 2'9  X IO“  V 3 (gr-ca1-)- 

6.  Debye’s  well  known  equation  is 

? = 7.4  x io7.A‘,/,.<r'/*.Kr,/!./(o)',/,( 

where /(o)  is  a function  of  Poisson’s  constant.  Debye  considers  v to  have 
a maximum  value,  which  is  the  one  given  by  the  equation.  The  other 
authorities  cited  consider  v to  have  only  one  value  under  definite  condi- 
tions. Blom  finds,  however,  that  the  more  exact  equation  of  Debye  does 
not  give  better  values,  since  the  data  involved  are  not  so  good  as  those  re- 
quired by  some  of  the  other  equations. 

Of  all  the  equations  given,  only  that  of  Lindemann  can  be  used  if  a com- 
parison including  nearly  all  of  the  elements  is  desired,  so  this  method 
of  calculation  has  been  chosen  for  the  data  plotted  in  Fig.  10.  About 
half  of  the  values  have  been  calculated  from  those  given  by  Biltz,2  who 
used  a different  constant,  and  the  rest  have  been  calculated  from  the 
other  data  given  in  Table  II. 

The  figure  shows  that  the  curve  has  a considerable  resemblance  to  that 
giving  the  reciprocals  of  the  melting  points  (Fig.  8).  The  greatest 
minimum  in  atomic  frequencies  (maximum  on  the  curve)  comes  at  helium, 
lesser  minima  at  neon  and  argon,  and  then  greater  minima  at  krypton, 
xenon  and  niton.  The  secondary  minima  come  at  gallium,  indium, 
mercury,  just  as  in  the  melting  point  curve.  The  maxima  occur  at  carbon, 
silicon,  titanium  to  nickel,  columbium  to  ruthenium,  tantalum,  and 
thorium  (U),  with  minor  maxima  at  germanium,  antimony,  and  thallium 
to  lead. 

As  has  been  pointed  out  by  Biltz,  carbon,  which  forms  the  greatest 
number  of  compounds  of  any  of  the  elements,  many  of  them  very  com- 
plex, has  by  far  the  highest  atomic  frequency  (37.0),  and  silicon,  which 
does  the  same  to  a lesser  degree,  is  also  at  a peak  in  the  frequency  curve, 
but  with  a value  only  about  one- third  of  that  of  carbon.  The  elements 
which  form  a large  number  of  complex  ammonia  compounds,  occur  at 
maxima  in  the  frequency  curve  (minima  in  the  reciprocal  curve).  Such 
elements  are  chromium,  cobalt,  platinum,  etc.  Further,  elements  just 
to  the  right  of  these  maxima,  on  descending  branches  of  the  frequency 
curve,  also  form  these  complexes.  Beryllium,  which  forms  very  stable 

1 Griineisen,  Ann.  Physik,  39,  293  (1912). 

2 Z.  Elektrochem.,  17,  170-4  (1911). 


43 


hexammines,  has  a very  high  frequency,  equal  to  23 . 4.  The  fact  that  on 
the  curve  hydrogen  has  the  same  relative  position  as  the  halogens,  is  taken 
by  Biltz1  to  indicate  that  it  belongs  to  the  halogen  group,  but  this  does 
not  prove  the  point,  since  in  chemical  behavior  hydrogen  is  not  like  the 
halogens.  A study  of  the  frequency  curve  will  reveal  many  other  rela- 
tions which  cannot  be  discussed  here. 

According  to  Equations  1,  2,  3 and  5,  the  following  quantities  must 
be  proportional  to  each  other: 


R 


and 


C, 

3<*V 


Blom1  considers  that  these  represent  the  cohesion  pressure.  He  plots 
the  logarithm  of  this  cohesion  pressure  for  each  of  these  functions,  and 
all  of  the  curves  have  exactly  the  general  form  which  the  curve  of  the 
reciprocals  of  the  atomic  frequencies  would  have  (Fig.  10)  if  it  were 
inverted.  A comparison  of  the  above  functions  shows  the  relationships 
which  exist.  Thus  from  (2)  and  (3)  Tm  = const,  a and  from  (2)  and  (5) 
Tm  — C v/a.  A number  of  these  relations  have  been  studied  by  Griineisen.2 
From  (1)  and  (2)  it  may  be  found  that  K = const.  V/Tm.  Richards  finds 
empirically  that  this  relation  does  not  contain  the  density  to  a high  enough 

A 

power,  and  that  the  expression  K = const. is  much  more 

F)l,25(Tm  — 50) 

exact.  In  order  to  correspond  more  closely  to  the  above  expressions 

V 

Richards’  equation  should  be  put  in  the  form  K = const. . 

(Tm  — 50)  D0-25 

This  equation  may  be  interpreted  to  mean  that  the  compressibility  varies 
not  only  as  the  atomic  volume,  and  as  the  reciprocal  of  the  melting  point, 
but  also  as  the  reciprocal  of  some  function  of  a quantity  which  varies  very 
nearly  as  the  density.  It  is  possible  that  this  quantity  is  the  number 
of  external  negative  electrons  in  the  gram  atom  divided  by  the  atomic 
weight,  or  the  number  of  external  negative  electrons  per  unit  volume. 
This  may  be  called  the  electronic  density  (de).  Reasoning  from  the 
standpoint  of  modern  theories  of  atomic  structure,  there  would  seem  to 
be  no  reason  why  the  density  of  the  material  itself  should  enter  into  the 
theoretical  equation  as  a modifying  factor  in  addition  to  its  occurrence 
in  the  atomic  volume,  but  it  is  easily  apparent  that  the  electronic  density 
might  be  a factor. 

An  empirical  equation  which  holds  as  well  as  that  given  by  Richards, 
for  the  sixteen  cases  for  which  he  calculates  the  values,3  and  which  is 
simpler,  is 

1 Loc.  cit. 

2 Ann.  Physik,  33,  33,  65  (19m);  39,  300  (1912). 

3 J.  Am.  Chem.  Soc.,  37,  1652  (1915). 


44 


Atomic  Nunoer  10  20  30  40  50  60  70  80  90  100 


45 


K = const.  

T D1-25 

Which  equation  gives  better  results  in  general  has  not  been  tested. 

Hardness. 

The  hardness  of  the  elements1  has  been  studied  by  Rydberg,  who  finds 
that  the  curve  for  hardness  has  the  general  form  of  the  melting  point 
curve,  or  of  the  curve  which  represents  cohesion  (Fig.  12).  The  minor 
differences  in  the  two  sets  of  curves  are  as  follows:  In  the  melting  point 
or  cohesion  curves  the  line  of  minor  minima  runs  gallium,  indium,  mer- 
cury, while  in  Rydberg’s  curve  of  hardness  it  runs  gallium,  indium, 
thallium,  but  this  difference  between  mercury  and  thallium  is  probably 
due  to  the  temperature  at  which  the  hardness  of  the  mercury  was  deter- 
mined as  compared  with  that  at  which  the  thallium  was  measured.  An- 
other point  of  difference  is  that  chromium  stands  very  much  higher  in 
the  curve  of  hardness  than  in  either  of  the  other  curves.  The  data  for 
hardness  are  very  inaccurate,  but  the  conclusion  is  inevitable  that  the 
hardness  is  proportional  to  some  function  of  the  cohesion.  Traube2 
finds  that  the  hardness  and  modulus  of  elasticity  also  run  parallel.  B lorn 3 
gives  curves  for  a number  of  oxides  of  the  type  RO,  and  shows  that 
when  the  mean  atomic  heat,  the  square  root  of  the  atomic  volume,  and 
the  softness  (reciprocal  of  the  hardness  on  Moh’s  scale)  are  plotted,  as 
functions  of  the  atomic  weights,  the  three  curves  have  the  same  form. 
The  same  relation  is  found  to  hold  for  oxides  of  the  form  R2O3. 

The  Elastic  Properties  of  the  Elements. 

Johnston4  gives  tables  which  show  that  for  the  twelve  metals  which  he 
considers,  the  hardness,  modulus  of  elasticity  (Young’s),  rigidity,  and 
tenacity,  all  increase  in  the  same  order,  and  in  the  order  in  which  the 
compressibility  decreases.  A study  of  the  elements  as  a whole,  shows 
that  somewhat  the  same  general  relations  hold  to  some  extent  for  elements 
which  are  not  metals,  but  the  exceptions  to  the  rule  are  numerous,  and 
the  magnitude  of  the  exception  is  often  considerable.  The  regularity 
of  the  behavior  of  the  metals  with  respect  to  these  properties  is  remarkable. 

Cohesion. 

A very  simple  experiment  upon  isotopes  would  give  much  light  as  to 
which  part  of  the  atom  by  its  variation  in  structure  or  mass,  conditions 
the  changes  in  cohesion.  Fig.  12  shows  the  variation  in  the  values 
of  Tm/V,  where  Tm  is  the  absolute  melting  point  and  V the  atomic  vol- 
ume. Blom3  claims  that  the  values  of  this  function  represent  the  cohe- 
sion. In  the  curve  the  logarithm  of  the  function  is  plotted,  since  other- 

1 Z.  physik.  Chem.,  33,  359  (1900). 

2 Z.  anorg.  Chem.,  34,  420-4  (1903). 

3 Loc.  cit. 

4 Z.  anorg.  Chem.,  76,  365  and  367  (1912). 


46 


Atomic  Nuait*  1 0 20  30  40  50  60  70  80  90  100 

Fig.  12. 


47 


wise  the  curve  for  the  function  itself  would  be  difficult  to  plot  on  one 
page.  Lindemann1  proves  by  thermodynamics,  on  the  basis  of  certain 
assumptions,  that  the  melting  points  of  isotopes  are  proportional  to  their 
atomic  weights.  According  to  this  conclusion  lead  from  thorium  should 
have  a melting  point  about  six  degrees  greater  than  that  of  lead  from 
radium.  Lindemann’s  result  may  be  stated  as  follows  in  terms  of  recent 
atomic  theories:  Whenever  the  nuclear  charge  remains  constant  the 
melting  point  and  the  cohesion  vary  as  the  mass  of  the  nucleus.  He 
concludes,  therefore,  that  “the  forces  of  attraction  and  repulsion  between 
atoms,  the  interaction  of  which  results  in  the  solid  state,  have  their  origin 
in  the  nucleus.”  Lindemann’s  calculation,  however,  involves  several 
doubtful  assumptions,  so  it  is  not  certain  that  his  conclusion  is  correct, 
and  it  may  be  well  to  consider  the  question  from  another  point  of  view. 

Following  out  his  line  of  reasoning,  it  could  be  predicted  that  if  an 
isotope  of  carbon,  of  atomic  number  six  (and  possibly  of  nuclear  charge 
six  also)  could  be  obtained  with  a mass  of  14,  its  melting  point  would  be 
about  4400  °.  If  this  should  then  undergo  a beta  change,  it  would  be- 
come nitrogen,  with  a melting  point  of  63  °,  or  of  about  one-seventieth  the 
melting  point  which  it  had  before  the  loss  of  the  one  negative  electron 
from  the  nucleus.  Presumably  when  the  nucleus  loses  a negative  elec- 
tron, the  number  of  external  electrons  increases  by  one  in  the  formation 
of  the  neutral  atom.  If  this  is  true,  a change  of  one  electron  from  the 
nucleus  into  an  external  electron,  without  a change  of  mass,  would  cause 
this  enormous  change  of  melting  point  amounting  to  more  than  4300  °, 
or  of  six  thousand  per  cent,  when  calculated  on  the  basis  of  the  melting 
point  of  nitrogen.  If  Lindemann’s  idea  is  on  the  other  hand  incorrect, 
and  if  isotopes  have  the  same  melting  points,  then  it  will  be  seen  that  the 
isotope  of  carbon  of  mass  14  would  have  a melting  point  of  about  3800°, 
and  the  melting  point  would  be  changed  about  sixtyfold  by  the  change 
of  one  electron  from  the  nucleus  to  the  external  region.  Changes  similar 
to  these  actually  occur  among  the  radioactive  elements,  but  the  changes 
of  melting  point  with  these  heavier  atoms  are  not  so  striking.  A single 
beta  change  (that  is  the  loss  of  an  electron  by  the  nucleus,  and  the  re- 
sultant increase  of  one  in  the  nuclear  charge,  and  probably  in  the  number 
of  external  electrons)  may  decrease  the  melting  point,  for  example,  in 
the  beta  change  from  an  isotope  of  lead  to  an  isotope  of  bismuth  the  de- 
crease is  56°,  or  in  another  case,  such  as  the  beta  change  of  thorium,  it 
may  increase  the  melting  point.  Thus  the  great  changes  of  cohesion 
which  occur  inside  of  one  period  in  the  periodic  system,  whether  of  electro- 
static or  of  electro-magnetic  origin,  and  more  probably  of  both,  must  de- 
pend much  more  on  the  arrangement  and  frequencies  of  the  particles, 
either  in  the  nucleus,  or  in  the  external  region  of  the  atom,  than  they  do 
1 Nature,  95,  7 (1915). 


48 


upon  the  changes  of  mass.  Thus,  in  the  first  period,  as  the  cohesion 
curve  shows,  there  occur  both  the  lowest  minimum  and  the  highest  maxi- 
mum in  cohesion  in  helium  and  carbon,  respectively,  elements  which  differ 
in  atomic  mass  by  only  eight.  It  is  evident  that  such  extreme  changes 
would  result  from  differences  in  arrangement  only  when  the  number  of 
electrons  is  small. 

The  question  under  consideration  here  is  not  the  origin  of  cohesion, 
but  of  its  variation  with  the  atomic  number.  This  variation  may  be 
caused  either  by  a change  in  arrangement  or  frequency  in  the  nucleus, 
or  among  the  external  electrons,  but  there  are  several  arguments  which 
seem  to  indicate  that  it  is  the  external  changes  which  are  the  important 
ones,  and  that  it  is  the  external  electrons  which  determine  the  spacing  of 
the  atoms,  and  therefore  the  atomic  volume.  It  is  evident,  of  course, 
that  it  is  the  nuclear  charge  which  determines  the  number  of  these  elec- 
trons, and  therefore  their  arrangement.  There  is  a very  close  relation 
between  the  variations  of  valence  in  the  periodic  system,  and  the  varia- 
tions in  cohesional  properties.  Since  the  valence  is  undoubtedly  condi- 
tioned by  electrons  external  to  the  nucleus,  it  is  probable  that  the  same  is 
true  of  the  related  cohesional  properties,  but  that  it  is  the  whole  system 
of  external  electrons  which  is  effective  in  the  latter  case.  The  nuclei 
of  atoms  fall  into  two  series,  which  differ  in  stability  according  as  the  atomic 
number  is  odd  or  even.  This  subject  will  be  more  fully  considered  in  a 
later  paper,  but  as  to  the  fact  there  is  no  doubt.  Now  neither  the  chem- 
ical nor  the  physical  properties  of  the  elements  show  this  marked  distinc- 
tion between  the  odd  and  even  numbered  elements,  which  -would  seem  to 
indicate  that  it  is  not  the  changes  in  the  nucleus  which  are  here  effective. 
On  the  other  hand,  it  must  be  realized  that  electromagnetic  effects  caused 
by  the  rotation  of  the  nucleus,  or  of  its  parts,  may  have  an  effect  upon  the 
arrangement  of  these  external  electrons. 

The  cohesion  is  not  a function  of  the  properties  of  the  atoms  alone, 
but  it  is  also  conditioned  by  the  form  of  the  space-lattice  in  the  solid,  as 
is  evident  if  graphite  and  the  diamond  are  compared. 

Magnetic  Susceptibility. 

In  Fig.  ii  the  susceptibilities  of  the  elements  per  unit  mass  times 
io7  have  been  plotted.  Most,  but  not  all,  of  the  data  were  taken  from 
a paper  by  M.  Owen.1  The  maxima  for  the  elements  of  positive  suscepti- 
bility come  with  oxygen,  and  then  an  extremely  high  maximum  in  the 
first  eighth  group,  Fe,  Co,  and  Ni.  The  next  maximum  is  not  nearly 
so  high,  but  comes  in  the  eighth  group  again  with  Pd.  After  this  there  is  a 
high  maximum  in  the  rare  earths,  a minor  maximum  in  the  eighth  group 
with  Pt,  and  a maximum  of  moderate  height  at  uranium.  It  is  interest- 
ing that  the  highest  maximum  is  in  the  eighth  group  the  first  time  it  ap- 
1 Ann.  Physik,  [4]  37,  657-99  (1912). 


49 


pears  in  the  system,  and  that  the  next  highest  maximum  comes  with  the 
first  and  only  appearance  of  the  rare  earth  group.  Both  of  these  groups 
are  related  to  each  other  in  that  in  them  the  valence  remains  constant 
as  the  atomic  number  increases  Neon,  not  determined  by  Owen,  seems 
to  be  a minimum  on  the  susceptibility  curve.  At  least  this  is  true  if  the 
experimental  work  is  trustworthy.  The  minima  found  by  Owen  are  Be, 
P,  Zr,  Sb,  and  Bi.  A rough  relationship  between  the  atomic  volume 
curve  and  the  susceptibility  curve  may  be  seen  by  bringing  the  two  to- 
gether, but  there  are  many  points  of  deviation  between  the  two.  A plot 
showing  the  atomic  magnetism  would  of  course  greatly  exaggerate  the 
deviations  from  the  zero  line  for  elements  of  high  atomic  weight. 

Fig.  1 1 is  interesting  in  that  it  proves  conclusively  that  the  old  stand- 
ard rule  that  elements  of  the  even  series  are  paramagnetic,  and  that  ele- 
ments of  the  odd  series  are  diamagnetic,  is  not  entirely  correct,  and  that, 
for  example,  the  susceptibility  changes  from  positive  to  negative  in  a sin- 
gle series.  The  fifth  series,  however,  seems  to  be  entirely  negative,  as  is 
also  the  seventh,  and  the  ninth,  as  far  as  it  is  known. 

Thus  in  the  short  periods  there  is  a change  from  diamagnetic  to  para- 
magnetic in  each  series , but  in  the  long  periods  beginning  with  argon, 
which  is  strongly  diamagnetic,  there  is  a first  jump  to  a slightly  para- 
magnetic substance  in  potassium.  Then  in  these  long  periods  the  ele- 
ments on  the  front  of  the  outer  loop  and  the  back  of  the  inner  loop  are  para- 
magnetic; those  on  the  front  of  the  inner  loop  and  the  back  of  the  outer  loop 
are  diamagnetic.  Beginning  with  the  long  periods,  the  iron  group  elements 
are  the  maxima  of  the  paramagnetic  elements  (with  an  additional  maximum 
in  the  rare  earths),  and  the  maxima  of  diamagnetism  in  all  probability  occur 
in  the  zero  group  elements.  Thus  the  zero  and  eighth  groups  form  the  two 
extremes  in  the  curve  representing  magnetic  properties,  just  as  they  do 
with  respect  to  atomic  volume,  cohesion,  and  related  properties.  This 
suggests  that  cohesion  is  partly  due  to  magnetic  forces.  That  it  is 
not  the  only  factor  involved  is,  however,  shown  by  the  many  deviations 
between  the  course  of  the  two  sets  of  curves.  Thus  carbon,  which  forms 
a maximum  in  the  cohesion  curve,  is  very  far  from  the  maximum  on  the 
susceptibility  curve. 

The  Number  of  Lines  in  the  Spectrum  of  an  Element. 

On  pages  36  and  37  of  their  book  “Die  Spektren  der  Elemente  bei 
Normalem  Druck,”  Volume  1,  Exner  and  Haschek  give  curves  showing 
the  relationship  between  the  atomic  weight  and  the  number  of  lines  in 
the  spectrum  of  an  element.  It  is  somewhat  difficult  to  see  just  how  they 
have  decided  upon  the  number  of  lines  in  each  case,  as  they  give  only 
one  line  for  the  spark  spectrum,  and  none  for  the  are  spectrum  of  hydro- 
gen, and  only  one  line  for  the  arc  spectrum  of  carbon.  The  values  of  such 
results  depend  upon  their  method  of  choosing  the  lines  to  be  counted. 


50 


They  find  that  the  curve  giving  the  number  of  lines  in  the  spark  spectrum 
has  maxima  at  V,  Mo,  W,  and  U,  and  this  falls  very  nearly  along  the  line 
of  maximum  melting  points.  Secondary  maxima  occur  at  Fe,  Nd,  Er  and 
Ir.  Of  all  of  the  elements  they  find  uranium  with  the  heaviest  atom 
and  the  greatest  number  of  external  electrons,  to  give  the  most  lines. 

Complex  Compounds  of  the  Periodic  System. 

It  is  a well-known  fact  that  the  elements  which  form  the  greatest  number 
of  compounds,  such  as  carbon  and  silicon,  are  elements  of  low  atomic  vol- 
ume. Thus  they  are  elements  of  high  cohesion,  and  they  also  have  a high 
valence. 


The  stability  of  a particular  type  of  complex  compounds  has  been 
studied  carefully  by  Ephraim,  who  measured  the  temperature  at  which 
the  vapor  pressure  of  ammonia  from  complex  metal  ammonia  compounds 
of  the  type  MX2.6NH3,  becomes  equal  to  500  mm. 


Table  III. — Temperatures  at  Which  the  Vapor  Pressures  of  Hexammine  Com- 
pound Becomes  Equal  to  500  mm. 


Dissociation  temperatures. 
Hexammines. 


Metal. 

Atomic 

volume. 

T m/V. 

Chlorides. 

Sulfates. 

Be 

5-3 

296.4 

High  temp. 

Ni 

6.7 

258.0 

165 

398 

Co 

6.7 

262  .0 

130 

378.5 

Fe 

7-1 

254-0 

106.5 

369 

Cu 

7-1 

191  -3 

95 

364-5 

Mn 

7-5 

204.0 

82 

340 

Zn 

9-2 

75-4 

5i 

299 

Cd 

131 

45-3 

50.5 

323-5 

Mg 

14.0 

66 

24-5 

... 

Hg,  Sn,  Pb 

>14 

<42 

Do  not  give 

comparable  com- 

Ca,  Sr,  Ba 

pounds  at  room  temperatures. 

For  any  one  series  investigated,  Ephraim1  finds  that  the  product  of  the 
cube  root  of  the  atomic  volume  (V1/s)  by  the  cube  root  of  the  tempera- 
ture of  decomposition  (TD1/3)  is  practically  a constant.  In  the  case  of 
the  substituted  ammonia  compounds,  the  stability  of  the  ammine  seems 
to  depend  also  upon  the  molecular  volume  of  the  organic  base.  The 
nature  of  the  anion  influences  the  stability. 

The  elements  which  form  complex  ammonia  compounds  belong,  mostly, 
in  the  inner  loop  of  the  periodic  table  (Figs.  1 and  2)  and  are  sub-group 
elements.  On  the  whole,  the  elements  at  the  left  of  the  inner  loop  form 
the  greatest  number  of  these  compounds.  That  the  stability  increases 
as  the  atomic  volume  of  the  metal  decreases,  is  apparent  from  Table  III, 
though  there  are  some  minor  exceptions  to  the  rule.  Thus  cadmium, 
with  an  atomic  volume  of  13. 1,  seems  to  form  a more  stable  hexammino- 
sulfate  than  zinc,  with  an  atomic  volume  of  9.2.  However,  the  ammino- 
1 Ber.,  45,  1323  (1912);  Z.  physik.  Chem.,  81,  513,  539  (1913);  83,  196  (1913)- 


5i 


chlorides  of  these  elements  follow  the  usual  rule.  The  values  of  Tm/V 
for  the  elements  which  represent  the  cohesion,  seem  to  be  in  as  close  a rela- 
tion to  the  dissociation  temperatures  of  the  chlorides  as  the  atomic 
volumes. 

Valence  and  Electroaffinity. 

The  important  subject  of  the  relation  between  the  periodic  system  and 
electroaffinity  has  been  so  thoroughly  treated  in  the  classic  papers  of 
Abegg  and  Bodlander,1  and  Abegg,2  that  it  need  not  be  considered  here. 
It  may  be  pointed  out  that  while  in  general,  in  any  one  group,  the  positive 
character  of  the  elements  increases  as  they  go  down  the  rod  on  which  they 
lie  in  the  table,  this  rule  is  reversed  for  those  elements  which  are  at  the 
left  (iron  group)  and  on  the  front  of  the  inner  loop  and  for  the  rare  earths. 
Thus  copper,  silver  and  gold  are  progressively  more  negative,  and  the 
same  is  true  of  iron,  ruthenium,  and  osmium,  and  also  of  zinc,  cadmium, 
and  mercury. 

Other  Properties  of  the  Elements. 

According  to  Cary  Lea,3  the  maxima  for  color  in  the  ions  formed  by  the 
elements  are  in  the  three-eighth  groups  and  in  the  rare  earth  group,  with 
a final  maximum  at  uranium.  This  is  interesting  in  so  far  as  it  is  true, 
in  that  this  relationship  is  similar  to  that  found  for  the  maxima  of  suscepti- 
bility, for  in  both  cases  the  maxima  occur  in  the  groups  where  the  valence 
remains  constant  as  the  atomic  number  rises. 


Other  properties  of  the  elements,  beside  those  discussed  in  this  paper, 
which  vary  in  a more  or  less  regular  way  with  their  position  in  the 
periodic  system,  are  given  in  the  following  list,  which,  however,  is  not 
complete : 


Electrical  conductivity4 
Conductivity  for  heat 
Boiling  points5 

Heats  of  chemical  combination6,7 


Electrode  potentials7 
Changes  of  volume  on  fusion8 
Solubility9 

Latent  heat  of  fusion10 


1 L.  Abegg,  “Die  Valenz  und  das  periodische  System  Versuch  einer  Theorie  der 
Molekularverbindungen,”  Z.  anorg.  Chem.,  39,  330-80  (1904). 

2 Abegg  and  Bodlander,  Ibid.,  20,  453-99. 

3 Chem.  News,  73,  203,  260-2  (1896);  Z.  anorg.  Chem.,  9,  312-28  (1895);  Am.  J. 
Sci.,  [3]  49,  357  (1895). 

4 Sander,  Elektrochem.  Z.,  6,  133. 

6  Carnelley,  Numerous  papers  in  Trans.  Chem.  Soc.,  Proc.  Roy.  Soc.  and  Phil. 
Mag.,  from  1876  on. 

6 Laurie,  Phil.  Mag.,  [5]  15,  42  (1883);  Richards,  Trans.  Chem.  Soc.,  99,  1201 
(1911);  Carnelley,  Phil.  Mag.,  [5]  18,  1-22  (1884). 

7 Abegg,  Z.  anorg.  Chem.,  39,  330-80  (1904). 

8 Topler,  Wied.  Ann.,  53,  343  (1894). 

9 Abegg  and  Bodlander,  Am.  Chem.  J.,  28,  220-8  (1902);  Locke,  Ibid.,  20, 
581-92  (1898);  26,  166-85,  332-45  (1901);  27,  455-81  (1902). 

10  Rudorf,  “Das  Periodische  Gesetz,”  pp.  143-9. 


52 


Ionic  mobilities1  Refractive  indices2 

Ultraviolet  vibration  frequencies5  Spectra3 

Mechanical  properties4 

Summary. 

1 . In  this  paper  a periodic  table  has  been  presented,  which  shows  graph- 
ically the  relations  between  the  main  and  the  sub-groups  of  elements. 
The  main  defect  of  the  periodic  tables  which  have  been  designed  formerly, 
is  that  they  do  not  show  these  relations  correctly. 

2.  The  table  arranges  the  elements  in  the  exact  order  of  their  atomic 
numbers,  and  gives  no  blanks  for  unknown  elements  which  do  not  corre- 
spond to  atomic  numbers  as  determined  by  Moseley’s  work  on  the  X-ray 
spectroscopy  of  the  elements. 

3.  It  also  plots  the  elements  according  to  their  atomic  weights,  so  the 
isotopic  forms  of  an  element  may  be  shown  graphically  on  the  table, 
and  the  alpha  and  beta  decompositions  of  the  radioactive  elements  may 
also  be  plainly  depicted. 

4.  Both  the  zero  and  the  eighth  groups  fit  naturally  into  the  system. 

5.  The  table  may  be  best  represented  as  a helix  in  space,  but  may  be 
shown  as  a spiral  in  a plane.  The  space  form  is  represented  by  its  vertical 
projection  on  a plane,  but  drawn  with  line  perspective  so  that  it  may 
easily  be  visualized. 

6.  Beginning  at  the  zero  group,  the  maximum  positive  valence  of  a 
group  is  found  by  counting  toward  the  front  and  toward  the  right,  Li  = 1 , 
Be  = 2,  etc.,  and  negative  valence  by  counting  toward  the  back,  Fe  = — 1, 
O = — 2,  N = — 3,  etc. 

7.  The  elements  in  the  table  divide  themselves  into  cycles, 

Cycle  o 

Cycle  1 = 42  elements 
Cycle  2 = 62  elements 
Cycle  3 = 82  elements 

but  the  latter  part  of  the  third  cycle  is  missing.  The  cycles  are  each 
divided  into  two  periods.  The  periods  are  as  follows: 

Period  Oi 

Period  O2 

Period  1 = 2 X 22 

2 = 2 X 22 

3 = 2 X 32 

4 = 2 X 32 

5 = 2 X 42 

6 = 2 X 42 

1 Bredig,  Z.  physik.  Chem.,  13,  289  (1894). 

2 Ibid.,  149-57;  Bishop,  Am.  Chem.  J.,  35,  84  (1906). 

3 Ibid.,  157-171;  Baly,  “Spectroscopy.” 

4 Ibid.,  187-96. 

6 Byk,  Ann.  Physik,  [4]  42,  1417-  53  (1913)- 


53 


These  relations  are  undoubtedly  a numerical  expression  of  a function 
connected  in  some  way  with  the  system  according  to  which  the  nuclei 
of  the  elements  have  been  built  up. 

8.  Whenever  the  valence  drops,  in  passing  along  the  continuous  line 
connecting  the  elements  in  the  order  of  their  atomic  numbers,  it  always 
drops  by  seven,  either  from  seven  to  zero,  or  from  eight  to  one.  In  the 
latter  case  there  is  evidenced  a certain  sluggishness  in  the  drop,  so  that  it 
is  not  entirely  complete,  so  that  copper,  silver  and  gold,  the  members  of 
which  should  have  the  maximum  valence  one,  often  exhibits  a higher 
valency,  such  as  two  for  copper  and  three  for  gold. 

9.  The  table  arranges  the  groups  into  5 divisions,  numbered  o,  1,  2, 
3,  4.  These  divisions  comprise  the  following  groups: 


Division 01234 

Groups 0.8  1.7  2.6  3.5  4.4 


The  two  groups  of  one  division  are  said  to  be  complementary.  The  sum 
of  the  group  numbers  of  two  complementary  groups  is  always  8,  as  is  also 
the  sum  of  the  maximum  valences.  The  algebraic  sum  of  their  charac- 
teristic valences  is,  on  the  other  hand,  always  zero.  Thus  the  characteris- 
tic valence  for  Group  1 is  +1,  and  for  Group  7 is  — 1.  The  characteristic 
valence  of  the  eighth  group  needs  to  be  defined  in  this  sense,  and  must  be 
taken  as  — o,  which  accords  with  Abegg’s  valence  system. 

10.  Another  very  important  relationship  given  graphically  in  this  table, 
and  not  at  all  by  any  other  which  the  writers  have  found,  is  that  between 
the  main  and  the  sub-groups  in  any  one  division.  Whenever  the  group 
numbers  in  any  one  division  differ  considerably,  as  is  the  case  in  divisions 
o and  1,  then  the  elements  in  the  sub-groups  are  quite  different  chemically 
from  the  members  of  the  main  group,  although  they  are  in  general  alike 
in  valence.  As  the  group  numbers  in  the  division  approach  each  other 
in  magnitude,  the  elements  of  the  sub-group  become  chemically  much 
like  those  of  the  main  group.  This  is  true  of  groups  4A  and  B,  where  the 
group  numbers  are  the  same,  and  the  two  groups  are  practically  indistin- 
guishable in  their  general  chemical  nature. 

11.  On  the  outer  cylinder  the  main  Groups  1,  2,  3 become  less  positive 
as  the  group  number  increases,  while  the  corresponding  sub-groups  be- 
come more  positive. 

12.  Whenever  the  atomic  volume  of  a main-group  element  is  large, 
that  of  the  corresponding  sub-group  element  is  small,  and  as  the  atomic 
volume  of  the  main  group  element  decreases,  that  of  the  sub-group  in- 
creases, until  the  values  become  about  the  same  in  Groups  4A  and  4B. 

13.  The  rare  earths  are  put  in  the  third  group,  since  their  valence  is 
three,  and  since  if  they  are  distributed  around  the  table  there  are  not 
enough  known  and  undiscovered  elements  together  to  go  around.  Cerium 
may  be  classified  either  with  the  third  or  the  fourth  group.  A discussion 


54 


of  this  minor  question  is  given.  The  elements  of  the  rare  earth  group  (not 
including  yttrium  or  cerium)  decrease  in  basic  properties  as  the  atomic 
weight  increases,  which  is  exactly  the  opposite  of  the  general  rule.  As 
has  been  explained  in  the  paper,  in  the  rare  earths  the  atomic  number, 
and  therefore  the  nuclear  charge,  keeps  on  increasing,  while  the  valence 
remains  constant.  On  the  other  hand,  it  seems  probable  that  the  atomic 
volume  tends  to  keep  on  as  it  usually  does,  but  this  tendency  is  masked 
partly  by  another  influence  which  tends  to  keep  the  atomic  volume  con- 
stant. The  rare  earths  lie  on  the  front  of  the  table,  where  the  elements  in 
general  become  less  basic  as  the  atomic  number  increases,  so  they,  in  this 
case,  as  they  probably  do  with  atomic  volumes,  effect  a compromise  be- 
tween this  tendency  and  that  which  seeks  to  cause  the  elements  in  a single 
group  to  become  more  basic  with  increase  in  atomic  weight.  The  resultant 
effect  is  that  they  become  less  basic  as  the  atomic  number  increases,  but 
not  with  anything  like  the  rapidity  which  would  be  shown  if  they  were 
to  go  around  the  table  in  the  usual  manner.  In  this  sense  the  rare  earth 
group  forms  a loop  of  its  own,  but  a loop  of  practically  constant  valence. 

14.  The  periodic  table  shows  the  relation  between  the  properties  of 
the  elements  and  the  nuclear  charge,  and  this  is  presumably  equal  to  the 
number  of  external  electrons.  It  is  probably  the  spacing  and  arrange- 
ment of  these  electrons  which  determines  the  chemical  and  most  of  the 
physical  properties  of  the  elements. 

15.  In  Table  II  it  maybe  seen  that  the  spiral  forms  a series  of  lines 
which  in  any  part  of  the  table  lie  very  nearly  parallel.  This  is  a graphical 
expression  of  the  well-known  fact  that  the  atomic  weights  increase  in  a 
very  regular  way  in  any  one  group,  and  at  about  the  same  rate  in  all  of 
the  groups.  This  regularity  may  be  explained  on  the  basis  of  the  theory 
of  Harkins  and  Wilson,  that  the  nuclei  of  the  elements  are  built  up  from 
hydrogen  and  helium  nuclei,  according  to  a regular  system,  according  to 
which  the  differences  in  mass  in  any  one  group  are  generally  due  wholly 
to  differences  in  the  number  of  helium  nuclei  present,  at  least  in  the  case 
of  the  lighter  elements. 

16.  In  Fig.  4 and  5 the  relations  of  the  radioactive  elements  to  the 
periodic  table  have  been  given.  The  nature  of  isotopes  is  discussed. 

17.  A number  of  figures  and  tables  have  been  given  to  illustrate  the  re- 
lationship between  the  cohesional  properties  of  the  elements  and  the 
periodic  system.  The  following  properties  have  been  plotted  graphically: 
Melting  points,  with  lines  of  maxima  and  primary  and  secondary  minima, 
atomic  volumes,  density,  cubic  coefficients  of  expansion,  compressibility, 
susceptibility,  atomic  frequency,  elastic  properties,  cohesion  and  hardness. 
For  the  discussion  of  the  relations  between  these  properties  the  body  of 
the  paper  should  be  consulted. 


55 


1 8.  A theory  as  to  the  factors  conditioning  variations  of  cohesion  is  given. 


19.  The  ordinary  theory,  that  the  atoms  in  solids  do  not  occupy  all  of 
the  space  is  supported. 

Several  problems  related  to  the  periodic  system  are  now  under  in- 
vestigation in  this  laboratory.  One  of  these  is  the  endeavor  to  prove 
whether  or  not  the  exceptional  atomic  weight  of  chlorine  is  due  to  its 
existence  in  two  isotopic  forms.  This  is  a very  important  problem  in 
its  bearing  on  the  theory  of  complex  atoms,  whatever  may  be  the  facts. 
Work  is  also  being  done  upon  the  melting  point  of  lead  derived  from  rad- 
ium. A third  problem  is  the  attempt  to  prove  whether  ordinary  lead  is  or 
is  not  a mixture  of  isotopes. 

The  writers  wish  to  thank  Mr.  W.  A.  Roberts  for  aid  in  the  construc- 
tion of  the  model  of  the  periodic  system. 

The  next  paper  in  this  series  will  be  on  “The  Evolution  of  the  Elements 
and  the  Stability  of  Complex  Atoms." 


3 0112  072896894 


